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Ingy döt Net 2023-07-01 11:58:00 -04:00
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Task/Sexy-primes/00-META.yaml Normal file
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---
from: http://rosettacode.org/wiki/Sexy_primes
note: Prime Numbers

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Task/Sexy-primes/00-TASK.txt Normal file
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In mathematics, '''sexy primes''' are prime numbers that differ from each other by six.
For example, the numbers '''5''' and '''11''' are both sexy primes, because '''11''' minus '''6''' is '''5'''.
The term "sexy prime" is a pun stemming from the Latin word for six: ''sex''.<br><br>
'''Sexy prime pairs:''' Sexy prime pairs are groups of two primes that differ by '''6'''. e.g. '''(5 11), (7 13), (11 17)'''<br>
See sequences: [[OEIS:A023201]] and [[OEIS:A046117]]<br><br>
'''Sexy prime triplets:''' Sexy prime triplets are groups of three primes where each differs from the next by '''6'''. e.g. '''(5 11 17), (7 13 19), (17 23 29)'''<br>
See sequences: [[OEIS:A046118]], [[OEIS:A046119]] and [[OEIS:A046120]]<br><br>
'''Sexy prime quadruplets:''' Sexy prime quadruplets are groups of four primes where each differs from the next by '''6'''. e.g. '''(5 11 17 23), (11 17 23 29)'''<br>
See sequences: [[OEIS:A023271]], [[OEIS:A046122]], [[OEIS:A046123]] and [[OEIS:A046124]]<br><br>
'''Sexy prime quintuplets:''' Sexy prime quintuplets are groups of five primes with a common difference of '''6'''. One of the terms must be divisible by '''5''', because '''5''' and '''6''' are relatively prime. Thus, the only possible sexy prime quintuplet is '''(5 11 17 23 29)'''<br><br>
;Task:
::*For each of pairs, triplets, quadruplets and quintuplets, Find and display the count of each group type of sexy primes less than one million thirty-five ('''1,000,035''').
::*Display at most the '''last''' '''5''', less than one million thirty-five, of each sexy prime group type.
::*Find and display the count of the unsexy primes less than one million thirty-five.
::*Find and display the '''last 10''' unsexy primes less than one million thirty-five.
::*Note that 1000033 '''SHOULD NOT''' be counted in the pair count. It is sexy, but not in a pair within the limit. However, it also '''SHOULD NOT''' be listed in the unsexy primes since it is sexy.
<br><br>

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Task/Sexy-primes/11l/sexy-primes.11l Normal file
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V LIMIT = 1'000'000
F get_primes(limit)
V is_prime = [0B] * 2 [+] [1B] * (limit - 1)
L(n) 0 .< Int(limit ^ 0.5 + 1.5)
I is_prime[n]
L(i) (n * n .< limit + 1).step(n)
is_prime[i] = 0B
R enumerate(is_prime).filter((i, prime) -> prime).map((i, prime) -> i)
V primes = get_primes(LIMIT)
V primeset = Set(primes)
V s = [[[Int]]()] * 4
[Int] unsexy
L(p) primes
I p + 6 C primeset
s[0].append([p, p + 6])
E
I p - 6 !C primeset
unsexy.append(p)
L.continue
I p + 12 C primeset
s[1].append([p, p + 6, p + 12])
E
L.continue
I p + 18 C primeset
s[2].append([p, p + 6, p + 12, p + 18])
E
L.continue
I p + 24 C primeset
s[3].append([p, p + 6, p + 12, p + 18, p + 24])
print(‘"SEXY" PRIME GROUPINGS:’)
L(sexy, name) zip(s, ‘pairs triplets quadruplets quintuplets’.split(‘ ’))
print(‘ #. #. ending with ...’.format(sexy.len, name))
L(sx) sexy[(len)-5..]
print(‘ ’sx)
print("\nThere are #. unsexy primes ending with ...".format(unsexy.len))
L(usx) unsexy[(len)-10..]
print(‘ ’usx)

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Task/Sexy-primes/ALGOL-W/sexy-primes.alg Normal file
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begin
% find some sexy primes - primes that differ from another prime by 6 %
% implements the sieve of Eratosthenes %
procedure sieve( logical array s ( * ); integer value n ) ;
begin
% start with everything flagged as prime %
for i := 1 until n do s( i ) := true;
% sieve out the non-primes %
s( 1 ) := false;
for i := 2 until truncate( sqrt( n ) ) do begin
if s( i ) then for p := i * i step i until n do s( p ) := false
end for_i ;
end sieve ;
% adds a prime to list of sexy/unsexy primes %
procedure addPrime ( integer value p
; integer array list ( * )
; integer value len
) ;
begin
% increment count, shuffle down the primes and add the new one %
list( 0 ) := list( 0 ) + 1;
for i := 1 until len - 1 do list( i ) := list( i + 1 );
list( len ) := p
end addPrime ;
% counts the number of pairs of sexy primes, triplets, quadruplest and %
% quintuplets up to n %
% the counts of each kind are returned in the 0 element of the arrays %
% the last 5 ( or less if there are less than 5 ) of each type of sexy %
% prime is returned in the array elements 1 to 5 %
procedure countSexyPrimes ( logical array s ( * )
; integer value n
; integer array pairs, triplets, quadruplets, quintuplets ( * )
) ;
begin
integer pos2, pos3, pos4, pos5;
for i := 0 until 5 do pairs( i ) := triplets( i ) := quadruplets( i ) := quintuplets( i ) := 0;
% look for pairs etc. up to n %
% 2 cannot be a sexy prime as it is the only even prime, thus: %
% pairs can start at 7, triplets at 13, quadruplets at 19 and %
% quintuplets at 25 %
for p := 7 step 2 until 11 do begin
if s( p ) and s( p - 6 ) then addPrime( p, pairs, 5 )
end for_p ;
for p := 13 step 2 until 17 do begin
if s( p ) and s( p - 6 ) then addPrime( p, pairs, 5 );
if s( p ) and s( p - 6 ) and s( p - 12 ) then addPrime( p, triplets, 5 )
end for_p ;
for p := 19 step 2 until 23 do begin
if s( p ) and s( p - 6 ) then addPrime( p, pairs, 5 );
if s( p ) and s( p - 6 ) and s( p - 12 ) then addPrime( p, triplets, 5 );
if s( p ) and s( p - 6 ) and s( p - 12 ) and s( p - 18 )
then addPrime( p, quadruplets, 5 )
end for_p ;
pos5 := 1;
pos4 := pos5 + 6;
pos3 := pos4 + 6;
pos2 := pos3 + 6;
for p := pos2 + 6 step 2 until n do begin
if s( p ) then begin
if s( pos2 ) then begin % sexy pair %
addPrime( p, pairs, 5 );
if s( pos3 ) then begin % sexy triplet %
addPrime( p, triplets, 5 );
if s( pos4 ) then begin % sexy quadruplet %
addPrime( p, quadruplets, 5 );
if s( pos5 ) then begin % sexy quintuplet %
addPrime( p, quintuplets, 5 )
end if_s_pos5
end if_s_pos4
end if_s_pos3
end if_s_pos2
end if_s_p ;
pos2 := pos2 + 2;
pos3 := pos3 + 2;
pos4 := pos4 + 2;
pos5 := pos5 + 2
end for_p
end countSexyPrimes ;
% counts the number of unsexy primes up to n %
% the count is returned in the 0 element of the array %
% the last 5 ( or less if there are less than 5 ) unsexy prime is %
% returned in the array elements 1 to 10 %
procedure countUnsexyPrimes ( logical array s ( * )
; integer value n
; integer array unsexy ( * )
) ;
begin
for i := 0 until 10 do unsexy( i ) := 0;
for p := 2, 3, 5 do begin % handle primes below 7 separately %
if s( p ) and not s( p + 6 ) then addPrime( p, unsexy, 10 )
end for_p ;
for p := 7 step 2 until n do begin
if s( p ) and not s( p - 6 ) and not s( p + 6 ) then addPrime( p, unsexy, 10 )
end for_p
end countUnsexyPrimes ;
% shows sexy prime pairs %
procedure showPrimes ( integer value elements
; integer array primes ( * )
; integer value arrayMax
; string(24) value title
; integer value maxPrime
) ;
begin
write( i_w := 8, s_w := 0, "Found ", primes( 0 ), " ", title, " below ", maxPrime + 1
, i_w := 2, "; last ", ( if primes( 0 ) > arrayMax then arrayMax else primes( 0 ) ), ":"
);
write( i_w := 1, s_w := 0, " " );
for p := 1 until arrayMax do begin
if primes( p ) not = 0 then begin
integer pn;
if elements > 1 then writeon( "(" );
pn := primes( p ) - ( ( elements - 1 ) * 6 );
for i := 1 until elements do begin
writeon( i_w := 1, s_w := 0, " ", pn );
pn := pn + 6
end for_i ;
if elements > 1 then writeon( " ) " );
end if_primes_p_ne_0
end for_p
end showPrimes ;
integer MAX_SEXY, MAX_PRIME;
% for the task, we need to consider primes up to 1 000 035 %
% however we must still recognise sexy primes up that limit, so we sieve %
% up to 1 000 035 + 6 %
MAX_SEXY := 1000000 + 35;
MAX_PRIME := MAX_SEXY + 6;
begin
logical array s ( 1 :: MAX_PRIME );
integer array pairs, triplets, quadruplets, quintuplets ( 0 :: 5 );
integer array unsexy ( 0 :: 10 );
sieve( s, MAX_PRIME );
countSexyPrimes( s, MAX_SEXY, pairs, triplets, quadruplets, quintuplets );
countUnsexyPrimes( s, MAX_SEXY, unsexy );
showPrimes( 2, pairs, 5, "sexy prime pairs", MAX_SEXY );
showPrimes( 3, triplets, 5, "sexy prime triplets", MAX_SEXY );
showPrimes( 4, quadruplets, 5, "sexy prime quadruplets", MAX_SEXY );
showPrimes( 5, quintuplets, 5, "sexy prime quintuplets", MAX_SEXY );
showPrimes( 1, unsexy, 10, "unsexy primes", MAX_SEXY )
end
end.

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Task/Sexy-primes/AWK/sexy-primes.awk Normal file
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# syntax: GAWK -f SEXY_PRIMES.AWK
BEGIN {
cutoff = 1000034
for (i=1; i<=cutoff; i++) {
n1 = i
if (is_prime(n1)) {
total_primes++
if ((n2 = n1 + 6) > cutoff) { continue }
if (is_prime(n2)) {
save(2,5,n1 FS n2)
if ((n3 = n2 + 6) > cutoff) { continue }
if (is_prime(n3)) {
save(3,5,n1 FS n2 FS n3)
if ((n4 = n3 + 6) > cutoff) { continue }
if (is_prime(n4)) {
save(4,5,n1 FS n2 FS n3 FS n4)
if ((n5 = n4 + 6) > cutoff) { continue }
if (is_prime(n5)) {
save(5,5,n1 FS n2 FS n3 FS n4 FS n5)
}
}
}
}
if ((s[2] s[3] s[4] s[5]) !~ (n1 "")) { # check for unsexy
save(1,10,n1)
}
}
}
printf("%d primes less than %s\n\n",total_primes,cutoff+1)
printf("%d unsexy primes\n%s\n\n",c[1],s[1])
printf("%d sexy prime pairs\n%s\n\n",c[2],s[2])
printf("%d sexy prime triplets\n%s\n\n",c[3],s[3])
printf("%d sexy prime quadruplets\n%s\n\n",c[4],s[4])
printf("%d sexy prime quintuplets\n%s\n\n",c[5],s[5])
exit(0)
}
function is_prime(x, i) {
if (x <= 1) {
return(0)
}
for (i=2; i<=int(sqrt(x)); i++) {
if (x % i == 0) {
return(0)
}
}
return(1)
}
function save(key,nbr_to_keep,str) {
c[key]++
str = s[key] str ", "
if (gsub(/,/,"&",str) > nbr_to_keep) {
str = substr(str,index(str,",")+2)
}
s[key] = str
}

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#include <array>
#include <iostream>
#include <vector>
#include <boost/circular_buffer.hpp>
#include "prime_sieve.hpp"
int main() {
using std::cout;
using std::vector;
using boost::circular_buffer;
using group_buffer = circular_buffer<vector<int>>;
const int max = 1000035;
const int max_group_size = 5;
const int diff = 6;
const int array_size = max + diff;
const int max_groups = 5;
const int max_unsexy = 10;
// Use Sieve of Eratosthenes to find prime numbers up to max
prime_sieve sieve(array_size);
std::array<int, max_group_size> group_count{0};
vector<group_buffer> groups(max_group_size, group_buffer(max_groups));
int unsexy_count = 0;
circular_buffer<int> unsexy_primes(max_unsexy);
vector<int> group;
for (int p = 2; p < max; ++p) {
if (!sieve.is_prime(p))
continue;
if (!sieve.is_prime(p + diff) && (p - diff < 2 || !sieve.is_prime(p - diff))) {
// if p + diff and p - diff aren't prime then p can't be sexy
++unsexy_count;
unsexy_primes.push_back(p);
} else {
// find the groups of sexy primes that begin with p
group.clear();
group.push_back(p);
for (int group_size = 1; group_size < max_group_size; group_size++) {
int next_p = p + group_size * diff;
if (next_p >= max || !sieve.is_prime(next_p))
break;
group.push_back(next_p);
++group_count[group_size];
groups[group_size].push_back(group);
}
}
}
for (int size = 1; size < max_group_size; ++size) {
cout << "number of groups of size " << size + 1 << " is " << group_count[size] << '\n';
cout << "last " << groups[size].size() << " groups of size " << size + 1 << ":";
for (const vector<int>& group : groups[size]) {
cout << " (";
for (size_t i = 0; i < group.size(); ++i) {
if (i > 0)
cout << ' ';
cout << group[i];
}
cout << ")";
}
cout << "\n\n";
}
cout << "number of unsexy primes is " << unsexy_count << '\n';
cout << "last " << unsexy_primes.size() << " unsexy primes:";
for (int prime : unsexy_primes)
cout << ' ' << prime;
cout << '\n';
return 0;
}

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Task/Sexy-primes/C++/sexy-primes-2.cpp Normal file
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#ifndef PRIME_SIEVE_HPP
#define PRIME_SIEVE_HPP
#include <algorithm>
#include <vector>
/**
* A simple implementation of the Sieve of Eratosthenes.
* See https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes.
*/
class prime_sieve {
public:
explicit prime_sieve(size_t);
bool is_prime(size_t) const;
private:
std::vector<bool> is_prime_;
};
/**
* Constructs a sieve with the given limit.
*
* @param limit the maximum integer that can be tested for primality
*/
inline prime_sieve::prime_sieve(size_t limit) {
limit = std::max(size_t(3), limit);
is_prime_.resize(limit/2, true);
for (size_t p = 3; p * p <= limit; p += 2) {
if (is_prime_[p/2 - 1]) {
size_t inc = 2 * p;
for (size_t q = p * p; q <= limit; q += inc)
is_prime_[q/2 - 1] = false;
}
}
}
/**
* Returns true if the given integer is a prime number. The integer
* must be less than or equal to the limit passed to the constructor.
*
* @param n an integer less than or equal to the limit passed to the
* constructor
* @return true if the integer is prime
*/
inline bool prime_sieve::is_prime(size_t n) const {
if (n == 2)
return true;
if (n < 2 || n % 2 == 0)
return false;
return is_prime_.at(n/2 - 1);
}
#endif

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#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <locale.h>
#define TRUE 1
#define FALSE 0
typedef unsigned char bool;
void sieve(bool *c, int limit) {
int i, p = 3, p2;
// TRUE denotes composite, FALSE denotes prime.
c[0] = TRUE;
c[1] = TRUE;
// no need to bother with even numbers over 2 for this task
for (;;) {
p2 = p * p;
if (p2 >= limit) {
break;
}
for (i = p2; i < limit; i += 2*p) {
c[i] = TRUE;
}
for (;;) {
p += 2;
if (!c[p]) {
break;
}
}
}
}
void printHelper(const char *cat, int len, int lim, int n) {
const char *sp = strcmp(cat, "unsexy primes") ? "sexy prime " : "";
const char *verb = (len == 1) ? "is" : "are";
printf("Number of %s%s less than %'d = %'d\n", sp, cat, lim, len);
printf("The last %d %s:\n", n, verb);
}
void printArray(int *a, int len) {
int i;
printf("[");
for (i = 0; i < len; ++i) printf("%d ", a[i]);
printf("\b]");
}
int main() {
int i, ix, n, lim = 1000035;
int pairs = 0, trips = 0, quads = 0, quins = 0, unsexy = 2;
int pr = 0, tr = 0, qd = 0, qn = 0, un = 2;
int lpr = 5, ltr = 5, lqd = 5, lqn = 5, lun = 10;
int last_pr[5][2], last_tr[5][3], last_qd[5][4], last_qn[5][5];
int last_un[10];
bool *sv = calloc(lim - 1, sizeof(bool)); // all FALSE by default
setlocale(LC_NUMERIC, "");
sieve(sv, lim);
// get the counts first
for (i = 3; i < lim; i += 2) {
if (i > 5 && i < lim-6 && !sv[i] && sv[i-6] && sv[i+6]) {
unsexy++;
continue;
}
if (i < lim-6 && !sv[i] && !sv[i+6]) {
pairs++;
} else continue;
if (i < lim-12 && !sv[i+12]) {
trips++;
} else continue;
if (i < lim-18 && !sv[i+18]) {
quads++;
} else continue;
if (i < lim-24 && !sv[i+24]) {
quins++;
}
}
if (pairs < lpr) lpr = pairs;
if (trips < ltr) ltr = trips;
if (quads < lqd) lqd = quads;
if (quins < lqn) lqn = quins;
if (unsexy < lun) lun = unsexy;
// now get the last 'x' for each category
for (i = 3; i < lim; i += 2) {
if (i > 5 && i < lim-6 && !sv[i] && sv[i-6] && sv[i+6]) {
un++;
if (un > unsexy - lun) {
last_un[un + lun - 1 - unsexy] = i;
}
continue;
}
if (i < lim-6 && !sv[i] && !sv[i+6]) {
pr++;
if (pr > pairs - lpr) {
ix = pr + lpr - 1 - pairs;
last_pr[ix][0] = i; last_pr[ix][1] = i + 6;
}
} else continue;
if (i < lim-12 && !sv[i+12]) {
tr++;
if (tr > trips - ltr) {
ix = tr + ltr - 1 - trips;
last_tr[ix][0] = i; last_tr[ix][1] = i + 6;
last_tr[ix][2] = i + 12;
}
} else continue;
if (i < lim-18 && !sv[i+18]) {
qd++;
if (qd > quads - lqd) {
ix = qd + lqd - 1 - quads;
last_qd[ix][0] = i; last_qd[ix][1] = i + 6;
last_qd[ix][2] = i + 12; last_qd[ix][3] = i + 18;
}
} else continue;
if (i < lim-24 && !sv[i+24]) {
qn++;
if (qn > quins - lqn) {
ix = qn + lqn - 1 - quins;
last_qn[ix][0] = i; last_qn[ix][1] = i + 6;
last_qn[ix][2] = i + 12; last_qn[ix][3] = i + 18;
last_qn[ix][4] = i + 24;
}
}
}
printHelper("pairs", pairs, lim, lpr);
printf(" [");
for (i = 0; i < lpr; ++i) {
printArray(last_pr[i], 2);
printf("\b] ");
}
printf("\b]\n\n");
printHelper("triplets", trips, lim, ltr);
printf(" [");
for (i = 0; i < ltr; ++i) {
printArray(last_tr[i], 3);
printf("\b] ");
}
printf("\b]\n\n");
printHelper("quadruplets", quads, lim, lqd);
printf(" [");
for (i = 0; i < lqd; ++i) {
printArray(last_qd[i], 4);
printf("\b] ");
}
printf("\b]\n\n");
printHelper("quintuplets", quins, lim, lqn);
printf(" [");
for (i = 0; i < lqn; ++i) {
printArray(last_qn[i], 5);
printf("\b] ");
}
printf("\b]\n\n");
printHelper("unsexy primes", unsexy, lim, lun);
printf(" [");
printArray(last_un, lun);
printf("\b]\n");
free(sv);
return 0;
}

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Task/Sexy-primes/F-Sharp/sexy-primes.fs Normal file
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// Sexy primes. Nigel Galloway: October 2nd., 2018
let n=pCache |> Seq.takeWhile(fun n->n<1000035) |> Seq.filter(fun n->(not (isPrime(n+6)) && (not isPrime(n-6))))) |> Array.ofSeq
printfn "There are %d unsexy primes less than 1,000,035. The last 10 are:" n.Length
Array.skip (n.Length-10) n |> Array.iter(fun n->printf "%d " n); printfn ""
let ni=pCache |> Seq.takeWhile(fun n->n<1000035) |> Seq.filter(fun n->isPrime(n-6)) |> Array.ofSeq
printfn "There are %d sexy prime pairs all components of which are less than 1,000,035. The last 5 are:" ni.Length
Array.skip (ni.Length-5) ni |> Array.iter(fun n->printf "(%d,%d) " (n-6) n); printfn ""
let nig=ni |> Array.filter(fun n->isPrime(n-12))
printfn "There are %d sexy prime triplets all components of which are less than 1,000,035. The last 5 are:" nig.Length
Array.skip (nig.Length-5) nig |> Array.iter(fun n->printf "(%d,%d,%d) " (n-12) (n-6) n); printfn ""
let nige=nig |> Array.filter(fun n->isPrime(n-18))
printfn "There are %d sexy prime quadruplets all components of which are less than 1,000,035. The last 5 are:" nige.Length
Array.skip (nige.Length-5) nige |> Array.iter(fun n->printf "(%d,%d,%d,%d) " (n-18) (n-12) (n-6) n); printfn ""
let nigel=nige |> Array.filter(fun n->isPrime(n-24))
printfn "There are %d sexy prime quintuplets all components of which are less than 1,000,035. The last 5 are:" nigel.Length
Array.skip (nigel.Length-5) nigel |> Array.iter(fun n->printf "(%d,%d,%d,%d,%d) " (n-24) (n-18) (n-12) (n-6) n); printfn ""

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USING: combinators.short-circuit fry interpolate io kernel
literals locals make math math.primes math.ranges prettyprint qw
sequences tools.memory.private ;
IN: rosetta-code.sexy-primes
CONSTANT: limit 1,000,035
CONSTANT: primes $[ limit primes-upto ]
CONSTANT: tuplet-names qw{ pair triplet quadruplet quintuplet }
: tuplet ( m n -- seq ) dupd 1 - 6 * + 6 <range> ;
: viable-tuplet? ( seq -- ? )
[ [ prime? ] [ limit < ] bi and ] all? ;
: sexy-tuplets ( n -- seq ) [ primes ] dip '[
[ _ tuplet dup viable-tuplet? [ , ] [ drop ] if ] each
] { } make ;
: ?last5 ( seq -- seq' ) 5 short tail* ;
: last5 ( seq -- str )
?last5 [ { } like unparse ] map " " join ;
:: tuplet-info ( n -- last5 l5-len num-tup limit tuplet-name )
n sexy-tuplets :> tup tup last5 tup ?last5 length tup length
commas limit commas n 2 - tuplet-names nth ;
: show-tuplets ( n -- )
tuplet-info
[I Number of sexy prime ${0}s < ${1}: ${2}I] nl
[I Last ${0}: ${1}I] nl nl ;
: unsexy-primes ( -- seq ) primes [
{ [ 6 + prime? not ] [ 6 - prime? not ] } 1&&
] filter ;
: show-unsexy ( -- )
unsexy-primes dup length commas limit commas
[I Number of unsexy primes < ${0}: ${1}I] nl
"Last 10: " write 10 short tail* [ pprint bl ] each nl ;
: main ( -- ) 2 5 [a,b] [ show-tuplets ] each show-unsexy ;
MAIN: main

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Task/Sexy-primes/FreeBASIC/sexy-primes.basic Normal file
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Function isPrime(Byval ValorEval As Uinteger) As Boolean
If ValorEval < 2 Then Return False
If ValorEval Mod 2 = 0 Then Return ValorEval = 2
If ValorEval Mod 3 = 0 Then Return ValorEval = 3
Dim d As Integer = 5
While d * d <= ValorEval
If ValorEval Mod d = 0 Then Return False Else d += 2
If ValorEval Mod d = 0 Then Return False Else d += 4
Wend
Return True
End Function
#define maxi 1000035
Dim As Integer CU = 0, C2 = 0, C3 = 0, C4 = 0, C5 = 0, N, I, P = 0
Dim As Integer Unsexy(10), Pairs(5), Trips(5), Quads(5), Quins(5)
For N = maxi To 2 Step -1
If isPrime(N) Then
P += 1
If Not isPrime(N-6) And Not isPrime(N+6) Then
If CU < 10 Then Unsexy(CU) = N
CU += 1
End If
If isPrime(N-6) Then
If C2 < 5 Then Pairs(C2) = N
C2 += 1
If isPrime(N-12) Then
If C3 < 5 Then Trips(C3) = N
C3 += 1
If isPrime(N-18) Then
If C4 < 5 Then Quads(C4) = N
C4 += 1
If isPrime(N-24) Then
If C5 < 5 Then Quins(C5) = N
C5 += 1
End If
End If
End If
End If
End If
Next N
Print P; " primes less than"; maxi
Print Chr(10); C2; " pairs ending with:"
For I = 4 To 0 Step -1
Print " [" & Pairs(I)-6 & ", "& Pairs(I) & "]"
Next I
Print Chr(10); C3; " triplets ending with:"
For I = 4 To 0 Step -1
Print " [" & Trips(I)-12 & ", "& Trips(I)-6 & ", "& Trips(I) & "]"
Next I
Print Chr(10); C4; " quadruplets ending with:"
For I = 4 To 0 Step -1
Print " [" & Quads(I)-18 & ", "& Quads(I)-12 & ", "& Quads(I)-6 & ", "& Quads(I) & "]"
Next I
Print Chr(10); C5; " quintuplet(s) ending with:"
I = Iif(C5 > 5, 5, C5)
For I = I-1 To 0 Step -1
Print " [" & Quins(I)-24 & ", "& Quins(I)-18 & ", "& Quins(I)-12 & ", "& Quins(I)-6 & ", "& Quins(I) & "]"
Next I
Print Chr(10); CU; " unsexy primes ending with:"
For I = 9 To 0 Step -1
Print Unsexy(I); ",";
Next I
Print Chr(8); " "
Sleep

113
Task/Sexy-primes/Go/sexy-primes.go Normal file
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package main
import "fmt"
func sieve(limit int) []bool {
limit++
// True denotes composite, false denotes prime.
c := make([]bool, limit) // all false by default
c[0] = true
c[1] = true
// no need to bother with even numbers over 2 for this task
p := 3 // Start from 3.
for {
p2 := p * p
if p2 >= limit {
break
}
for i := p2; i < limit; i += 2 * p {
c[i] = true
}
for {
p += 2
if !c[p] {
break
}
}
}
return c
}
func commatize(n int) string {
s := fmt.Sprintf("%d", n)
if n < 0 {
s = s[1:]
}
le := len(s)
for i := le - 3; i >= 1; i -= 3 {
s = s[0:i] + "," + s[i:]
}
if n >= 0 {
return s
}
return "-" + s
}
func printHelper(cat string, le, lim, max int) (int, int, string) {
cle, clim := commatize(le), commatize(lim)
if cat != "unsexy primes" {
cat = "sexy prime " + cat
}
fmt.Printf("Number of %s less than %s = %s\n", cat, clim, cle)
last := max
if le < last {
last = le
}
verb := "are"
if last == 1 {
verb = "is"
}
return le, last, verb
}
func main() {
lim := 1000035
sv := sieve(lim - 1)
var pairs [][2]int
var trips [][3]int
var quads [][4]int
var quins [][5]int
var unsexy = []int{2, 3}
for i := 3; i < lim; i += 2 {
if i > 5 && i < lim-6 && !sv[i] && sv[i-6] && sv[i+6] {
unsexy = append(unsexy, i)
continue
}
if i < lim-6 && !sv[i] && !sv[i+6] {
pair := [2]int{i, i + 6}
pairs = append(pairs, pair)
} else {
continue
}
if i < lim-12 && !sv[i+12] {
trip := [3]int{i, i + 6, i + 12}
trips = append(trips, trip)
} else {
continue
}
if i < lim-18 && !sv[i+18] {
quad := [4]int{i, i + 6, i + 12, i + 18}
quads = append(quads, quad)
} else {
continue
}
if i < lim-24 && !sv[i+24] {
quin := [5]int{i, i + 6, i + 12, i + 18, i + 24}
quins = append(quins, quin)
}
}
le, n, verb := printHelper("pairs", len(pairs), lim, 5)
fmt.Printf("The last %d %s:\n %v\n\n", n, verb, pairs[le-n:])
le, n, verb = printHelper("triplets", len(trips), lim, 5)
fmt.Printf("The last %d %s:\n %v\n\n", n, verb, trips[le-n:])
le, n, verb = printHelper("quadruplets", len(quads), lim, 5)
fmt.Printf("The last %d %s:\n %v\n\n", n, verb, quads[le-n:])
le, n, verb = printHelper("quintuplets", len(quins), lim, 5)
fmt.Printf("The last %d %s:\n %v\n\n", n, verb, quins[le-n:])
le, n, verb = printHelper("unsexy primes", len(unsexy), lim, 10)
fmt.Printf("The last %d %s:\n %v\n\n", n, verb, unsexy[le-n:])
}

37
Task/Sexy-primes/Haskell/sexy-primes-1.hs Normal file
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import Text.Printf (printf)
import Data.Numbers.Primes (isPrime, primes)
type Pair = (Int, Int)
type Triplet = (Int, Int, Int)
type Quad = (Int, Int, Int, Int)
type Quin = (Int, Int, Int, Int, Int)
type Result = ([Pair], [Triplet], [Quad], [Quin], [Int])
groups :: Int -> Result -> Result
groups n r@(p, t, q, qn, u)
| isPrime n4 && isPrime n3 && isPrime n2 && isPrime n1 = (addPair, addTriplet, addQuad, addQuin, u)
| isPrime n3 && isPrime n2 && isPrime n1 = (addPair, addTriplet, addQuad, qn, u)
| isPrime n2 && isPrime n1 = (addPair, addTriplet, q, qn, u)
| isPrime n1 = (addPair, t, q, qn, u)
| not (isPrime (n+6)) && not (isPrime n1) = (p, t, q, qn, n : u)
| otherwise = r
where addPair = (n1, n) : p
addTriplet = (n2, n1, n) : t
addQuad = (n3, n2, n1, n) : q
addQuin = (n4, n3, n2, n1, n) : qn
n1 = n - 6
n2 = n - 12
n3 = n - 18
n4 = n - 24
main :: IO ()
main = do
printf ("Number of sexy prime pairs: %d\n" <> lastFiveText) (length pairs) (lastFive pairs)
printf ("Number of sexy prime triplets: %d\n" <> lastFiveText) (length triplets) (lastFive triplets)
printf ("Number of sexy prime quadruplets: %d\n" <> lastFiveText) (length quads) (lastFive quads)
printf "Number of sexy prime quintuplets: %d\n Last 1 : %s\n\n" (length quins) (show $ last quins)
printf "Number of unsexy primes: %d\n Last 10: %s\n\n" (length unsexy) (show $ drop (length unsexy - 10) unsexy)
where (pairs, triplets, quads, quins, unsexy) = foldr groups ([], [], [], [], []) $ takeWhile (< 1000035) primes
lastFive xs = show $ drop (length xs - 5) xs
lastFiveText = " Last 5 : %s\n\n"

50
Task/Sexy-primes/Haskell/sexy-primes-2.hs Normal file
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{-# LANGUAGE TemplateHaskell #-}
import Control.Lens (makeLenses, over, (^.), to, view)
import Data.Numbers.Primes (isPrime, primes)
import Text.Printf (printf)
data Group a = Group { _count :: Int, _results :: [a] } deriving (Show)
makeLenses ''Group
type Groups = ( Group (Int, Int)
, Group (Int, Int, Int)
, Group (Int, Int, Int, Int)
, Group (Int, Int, Int, Int, Int)
, Group Int )
initialGroups :: Groups
initialGroups = let newGroup = Group 0 []
in (newGroup, newGroup, newGroup, newGroup, newGroup)
collect :: Groups -> Int -> Groups
collect r@(pr, tt, qd, qn, un) n
| isPrime n4 && isPrime n3 && isPrime n2 && isPrime n1 = (addPair pr, addTriplet tt, addQuad qd, addQuin qn, un)
| isPrime n3 && isPrime n2 && isPrime n1 = (addPair pr, addTriplet tt, addQuad qd, qn, un)
| isPrime n2 && isPrime n1 = (addPair pr, addTriplet tt, qd, qn, un)
| isPrime n1 = (addPair pr, tt, qd, qn, un)
| not (isPrime (n+6)) && not (isPrime n1) = (pr, tt, qd, qn, addUnSexy un)
| otherwise = r
where
n1 = n-6
n2 = n-12
n3 = n-18
n4 = n-24
addPair = over count succ . over results (take 5 . (:) (n1, n))
addTriplet = over count succ . over results (take 5 . (:) (n2, n1, n))
addQuad = over count succ . over results (take 5 . (:) (n3, n2, n1, n))
addQuin = over count succ . over results (take 1 . (:) (n4, n3, n2, n1, n))
addUnSexy = over count succ . over results (take 10 . (:) n)
main :: IO ()
main = do
let (pr, tt, qd, qn, un) = collectGroups primes
printf "Number of sexy prime pairs: %d\n Last 5 : %s\n\n" (pr ^. count) (pr ^. results . to display)
printf "Number of sexy prime triplets: %d\n Last 5 : %s\n\n" (tt ^. count) (tt ^. results . to display)
printf "Number of sexy prime quadruplets: %d\n Last 5 : %s\n\n" (qd ^. count) (qd ^. results . to display)
printf "Number of sexy prime quintuplets: %d\n Last 1 : %s\n\n" (qn ^. count) (qn ^. results . to display)
printf "Number of unsexy primes: %d\n Last 10: %s\n\n" (un ^. count) (un ^. results . to display)
where
collectGroups = foldl collect initialGroups . takeWhile (< 1000035)
display :: Show a => [a] -> String
display = show . reverse

31
Task/Sexy-primes/J/sexy-primes-1.j Normal file
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#sp2=: (#~ 1 p: _6+]) p1=:i.&.(p:inv) 1000035 NB. pairs
16386
(_6*i.-2)+/_5{.sp2
999371 999431 999721 999763 999953
999377 999437 999727 999769 999959
#sp3=: (#~ 1 p: _12+]) sp2 NB. triplets
2900
(_6*i.-3)+/_5{.sp3
997427 997541 998071 998617 998737
997433 997547 998077 998623 998743
997439 997553 998083 998629 998749
#sp4=: (#~ 1 p: _18+]) sp3 NB. quads
325
(_6*i.-5)+/_5{.sp4
977345 983765 986125 990365 997085
977351 983771 986131 990371 997091
977357 983777 986137 990377 997097
977363 983783 986143 990383 997103
977369 983789 986149 990389 997109
#sp5=: (#~ 1 p: _24+]) sp4 NB. quint
1
(_6*i.5)+/sp5
29
23
17
11
5
#unp=: p1-. 0 6+/(#~ 1 p: 6+]) p1
48627
_10{.unp
999853 999863 999883 999907 999917 999931 999961 999979 999983 1000003

27
Task/Sexy-primes/J/sexy-primes-2.j Normal file
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NB. Primes Not Greater Than (the input)
NB. The 1 _1 p: ... logic here allows the input value to
NB. be included in the list in the case it itself is prime
pngt =: p:@:i.@:([: +/ 1 _1 p:"0 ])
NB. Add 6 and see which sums appear in input list
sexy =: ] #~ + e. ]
NB. Iterate "sexy" logic up to orgy size
orgy =: sexy&.>^:( ({.@:[) ` (<@:{:@:[) ` (<@:]) )
sp =: dyad define
'pd os' =. x NB. x is prime distance (6), orgy size (5)
p =. pngt y
o =. x orgy p
g =. o +/&.> <\ +/\ _1 |.!.0 os # pd NB. Groups
's g' =. split g NB. Split singles from groups
l =. (({.~ -) 5 <. #)&.> g NB. Last (max) 5 groups
NB. I'm sure there's something clever with p-.s or similar,
NB. but (a) I don't want to think through it, and (b)
NB. it causes the kind of edge-case issues the spec warns
NB. about with 1000033
us =. p (] #~ 1 +:/@:p: +/)~ (+,-) pd NB. Unsexy numbers
( (# ; _10&{.) us ) , (#&.> g) ,. l
)

27
Task/Sexy-primes/J/sexy-primes-3.j Normal file
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r =: 6 5 sp 1000035 NB. 6=sex=prime distance, 5=max orgy size
(;:'Group Count Examples') , (;:'Unsexy Pairs Triplets Quadruplets Quintuplets') ,. r
+-----------+-----+----------------------------------------------------------------------+
|Group |Count|Examples |
+-----------+-----+----------------------------------------------------------------------+
|Unsexy |48627|999853 999863 999883 999907 999917 999931 999961 999979 999983 1000003|
+-----------+-----+----------------------------------------------------------------------+
|Pairs |16386|999371 999377 |
| | |999431 999437 |
| | |999721 999727 |
| | |999763 999769 |
| | |999953 999959 |
+-----------+-----+----------------------------------------------------------------------+
|Triplets |2900 |997427 997433 997439 |
| | |997541 997547 997553 |
| | |998071 998077 998083 |
| | |998617 998623 998629 |
| | |998737 998743 998749 |
+-----------+-----+----------------------------------------------------------------------+
|Quadruplets|325 |977351 977357 977363 977369 |
| | |983771 983777 983783 983789 |
| | |986131 986137 986143 986149 |
| | |990371 990377 990383 990389 |
| | |997091 997097 997103 997109 |
+-----------+-----+----------------------------------------------------------------------+
|Quintuplets|1 |5 11 17 23 29 |
+-----------+-----+----------------------------------------------------------------------+

73
Task/Sexy-primes/Java/sexy-primes.java Normal file
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import java.util.ArrayList;
import java.util.List;
public class SexyPrimes {
public static void main(String[] args) {
sieve();
int pairs = 0;
List<String> pairList = new ArrayList<>();
int triples = 0;
List<String> tripleList = new ArrayList<>();
int quadruplets = 0;
List<String> quadrupletList = new ArrayList<>();
int unsexyCount = 1; // 2 (the even prime) not found in tests below.
List<String> unsexyList = new ArrayList<>();
for ( int i = 3 ; i < MAX ; i++ ) {
if ( i-6 >= 3 && primes[i-6] && primes[i] ) {
pairs++;
pairList.add((i-6) + " " + i);
if ( pairList.size() > 5 ) {
pairList.remove(0);
}
}
else if ( i < MAX-2 && primes[i] && ! (i+6<MAX && primes[i] && primes[i+6])) {
unsexyCount++;
unsexyList.add("" + i);
if ( unsexyList.size() > 10 ) {
unsexyList.remove(0);
}
}
if ( i-12 >= 3 && primes[i-12] && primes[i-6] && primes[i] ) {
triples++;
tripleList.add((i-12) + " " + (i-6) + " " + i);
if ( tripleList.size() > 5 ) {
tripleList.remove(0);
}
}
if ( i-16 >= 3 && primes[i-18] && primes[i-12] && primes[i-6] && primes[i] ) {
quadruplets++;
quadrupletList.add((i-18) + " " + (i-12) + " " + (i-6) + " " + i);
if ( quadrupletList.size() > 5 ) {
quadrupletList.remove(0);
}
}
}
System.out.printf("Count of sexy triples less than %,d = %,d%n", MAX, pairs);
System.out.printf("The last 5 sexy pairs:%n %s%n%n", pairList.toString().replaceAll(", ", "], ["));
System.out.printf("Count of sexy triples less than %,d = %,d%n", MAX, triples);
System.out.printf("The last 5 sexy triples:%n %s%n%n", tripleList.toString().replaceAll(", ", "], ["));
System.out.printf("Count of sexy quadruplets less than %,d = %,d%n", MAX, quadruplets);
System.out.printf("The last 5 sexy quadruplets:%n %s%n%n", quadrupletList.toString().replaceAll(", ", "], ["));
System.out.printf("Count of unsexy primes less than %,d = %,d%n", MAX, unsexyCount);
System.out.printf("The last 10 unsexy primes:%n %s%n%n", unsexyList.toString().replaceAll(", ", "], ["));
}
private static int MAX = 1_000_035;
private static boolean[] primes = new boolean[MAX];
private static final void sieve() {
// primes
for ( int i = 2 ; i < MAX ; i++ ) {
primes[i] = true;
}
for ( int i = 2 ; i < MAX ; i++ ) {
if ( primes[i] ) {
for ( int j = 2*i ; j < MAX ; j += i ) {
primes[j] = false;
}
}
}
}
}

36
Task/Sexy-primes/Jq/sexy-primes.jq Normal file
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include "primeSieve"; # or copy-and-paste its def
def when(filter; action): if filter // null then action else . end;
def results($cat; $lim; $max; $array):
($array|length) as $len
| (if $cat != "unsexy primes" then "sexy prime " + $cat else $cat end) as $cat
| (if $len < $max then $len else $max end) as $last
| (if $last == 1 then "is" else "are" end) as $verb
| "Number of \($cat) less than \($lim) = \($len)",
"The last \($max) \($verb):\n \($array[ - $last :])\n";
def task($lim):
(($lim-1) | primeSieve) as $sieve # $sieve[i] iff i is prime
| { pairs:[], trips:[], quads:[], quins:[], unsexy:[2, 3], i: 3 }
| until (.i >= $lim;
if .i > 5 and .i < $lim-6 and $sieve[.i] and ($sieve[.i-6]|not) and ($sieve[.i+6]|not)
then .unsexy += [.i]
else when(.i < $lim-6 and $sieve[.i] and $sieve[.i+6];
.pairs += [[.i, .i+6]]
| when(.i < $lim-12 and $sieve[.i+12];
.trips += [[.i, .i+6, .i+12]]
| when(.i < $lim-18 and $sieve[.i+18];
.quads += [[.i, .i+6, .i+12, .i+18]]
| when(.i < $lim-24 and $sieve[.i+24];
.quins += [[.i, .i+6, .i+12, .i+18, .i+24]]))))
end
| .i += 2 )
| results("pairs"; $lim; 5; .pairs),
results("triplets"; $lim; 5; .trips),
results("quadruplets"; $lim; 5; .quads),
results("quintuplets"; $lim; 5; .quins),
results("unsexy primes"; $lim; 10; .unsexy)
;
task(1000035)

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Task/Sexy-primes/Julia/sexy-primes.julia Normal file
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using Primes
function nextby6(n, a)
top = length(a)
i = n + 1
j = n + 2
k = n + 3
if n >= top
return n
end
possiblenext = a[n] + 6
if i <= top && possiblenext == a[i]
return i
elseif j <= top && possiblenext == a[j]
return j
elseif k <= top && possiblenext == a[k]
return k
end
return n
end
function lastones(dict, n)
arr = sort(collect(keys(dict)))
beginidx = max(1, length(arr) - n + 1)
arr[beginidx: end]
end
function lastoneslessthan(dict, n, ceiling)
arr = filter(y -> y < ceiling, lastones(dict, n+3))
beginidx = max(1, length(arr) - n + 1)
arr[beginidx: end]
end
function primesbysexiness(x)
twins = Dict{Int64, Array{Int64,1}}()
triplets = Dict{Int64, Array{Int64,1}}()
quadruplets = Dict{Int64, Array{Int64,1}}()
quintuplets = Dict{Int64, Array{Int64,1}}()
possibles = primes(x + 30)
singles = filter(y -> y <= x - 6, possibles)
unsexy = Dict(p => true for p in singles)
for (i, p) in enumerate(singles)
twinidx = nextby6(i, possibles)
if twinidx > i
delete!(unsexy, p)
delete!(unsexy, p + 6)
twins[p] = [i, twinidx]
tripidx = nextby6(twinidx, possibles)
if tripidx > twinidx
triplets[p] = [i, twinidx, tripidx]
quadidx = nextby6(tripidx, possibles)
if quadidx > tripidx
quadruplets[p] = [i, twinidx, tripidx, quadidx]
quintidx = nextby6(quadidx, possibles)
if quintidx > quadidx
quintuplets[p] = [i, twinidx, tripidx, quadidx, quintidx]
end
end
end
end
end
# Find and display the count of each group
println("There are:\n$(length(twins)) twins,\n",
"$(length(triplets)) triplets,\n",
"$(length(quadruplets)) quadruplets, and\n",
"$(length(quintuplets)) quintuplets less than $x.")
println("The last 5 twin primes start with ", lastoneslessthan(twins, 5, x - 6))
println("The last 5 triplet primes start with ", lastones(triplets, 5))
println("The last 5 quadruplet primes start with ", lastones(quadruplets, 5))
println("The quintuplet primes start with ", lastones(quintuplets, 5))
println("There are $(length(unsexy)) unsexy primes less than $x.")
lastunsexy = sort(collect(keys(unsexy)))[length(unsexy) - 9: end]
println("The last 10 unsexy primes are: $lastunsexy")
end
primesbysexiness(1000035)

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Task/Sexy-primes/Kotlin/sexy-primes.kotlin Normal file
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// Version 1.2.71
fun sieve(lim: Int): BooleanArray {
var limit = lim + 1
// True denotes composite, false denotes prime.
val c = BooleanArray(limit) // all false by default
c[0] = true
c[1] = true
// No need to bother with even numbers over 2 for this task.
var p = 3 // Start from 3.
while (true) {
val p2 = p * p
if (p2 >= limit) break
for (i in p2 until limit step 2 * p) c[i] = true
while (true) {
p += 2
if (!c[p]) break
}
}
return c
}
fun printHelper(cat: String, len: Int, lim: Int, max: Int): Pair<Int, String> {
val cat2 = if (cat != "unsexy primes") "sexy prime " + cat else cat
System.out.printf("Number of %s less than %d = %,d\n", cat2, lim, len)
val last = if (len < max) len else max
val verb = if (last == 1) "is" else "are"
return last to verb
}
fun main(args: Array<String>) {
val lim = 1_000_035
val sv = sieve(lim - 1)
val pairs = mutableListOf<List<Int>>()
val trips = mutableListOf<List<Int>>()
val quads = mutableListOf<List<Int>>()
val quins = mutableListOf<List<Int>>()
val unsexy = mutableListOf(2, 3)
for (i in 3 until lim step 2) {
if (i > 5 && i < lim - 6 && !sv[i] && sv[i - 6] && sv[i + 6]) {
unsexy.add(i)
continue
}
if (i < lim - 6 && !sv[i] && !sv[i + 6]) {
val pair = listOf(i, i + 6)
pairs.add(pair)
} else continue
if (i < lim - 12 && !sv[i + 12]) {
val trip = listOf(i, i + 6, i + 12)
trips.add(trip)
} else continue
if (i < lim - 18 && !sv[i + 18]) {
val quad = listOf(i, i + 6, i + 12, i + 18)
quads.add(quad)
} else continue
if (i < lim - 24 && !sv[i + 24]) {
val quin = listOf(i, i + 6, i + 12, i + 18, i + 24)
quins.add(quin)
}
}
var (n2, verb2) = printHelper("pairs", pairs.size, lim, 5)
System.out.printf("The last %d %s:\n %s\n\n", n2, verb2, pairs.takeLast(n2))
var (n3, verb3) = printHelper("triplets", trips.size, lim, 5)
System.out.printf("The last %d %s:\n %s\n\n", n3, verb3, trips.takeLast(n3))
var (n4, verb4) = printHelper("quadruplets", quads.size, lim, 5)
System.out.printf("The last %d %s:\n %s\n\n", n4, verb4, quads.takeLast(n4))
var (n5, verb5) = printHelper("quintuplets", quins.size, lim, 5)
System.out.printf("The last %d %s:\n %s\n\n", n5, verb5, quins.takeLast(n5))
var (nu, verbu) = printHelper("unsexy primes", unsexy.size, lim, 10)
System.out.printf("The last %d %s:\n %s\n\n", nu, verbu, unsexy.takeLast(nu))
}

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Task/Sexy-primes/Lua/sexy-primes.lua Normal file
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local N = 1000035
-- FUNCS:
local function T(t) return setmetatable(t, {__index=table}) end
table.filter = function(t,f) local s=T{} for _,v in ipairs(t) do if f(v) then s[#s+1]=v end end return s end
table.map = function(t,f,...) local s=T{} for _,v in ipairs(t) do s[#s+1]=f(v,...) end return s end
table.lastn = function(t,n) local s=T{} n=n>#t and #t or n for i = 1,n do s[i]=t[#t-n+i] end return s end
table.each = function(t,f,...) for _,v in ipairs(t) do f(v,...) end end
-- PRIMES:
local sieve, primes = {false}, T{}
for i = 2,N+6 do sieve[i]=true end
for i = 2,N+6 do if sieve[i] then for j=i*i,N+6,i do sieve[j]=nil end end end
for i = 2,N+6 do if sieve[i] then primes[#primes+1]=i end end
-- TASKS:
local sexy, name = { primes }, { "primes", "pairs", "triplets", "quadruplets", "quintuplets" }
local function sexy2str(v,n) local s=T{} for i=1,n do s[i]=v+(i-1)*6 end return "("..s:concat(" ")..")" end
for i = 2, 5 do
sexy[i] = sexy[i-1]:filter(function(v) return v+(i-1)*6<N and sieve[v+(i-1)*6] end)
print(#sexy[i] .. " " .. name[i] .. ", ending with: " .. sexy[i]:lastn(5):map(sexy2str,i):concat(" "))
end
local unsexy = primes:filter(function(v) return not (v>=N or sieve[v-6] or sieve[v+6]) end)
print(#unsexy .. " unsexy, ending with: " ..unsexy:lastn(10):concat(" "))

31
Task/Sexy-primes/Mathematica/sexy-primes.math Normal file
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ClearAll[AllSublengths]
AllSublengths[l_List] := If[Length[l] > 2,
Catenate[Partition[l, #, 1] & /@ Range[2, Length[l]]]
,
{l}
]
primes = Prime[Range[PrimePi[1000035]]];
ps = Union[Intersection[primes + 6, primes] - 6, Intersection[primes - 6, primes] + 6];
a = Intersection[ps + 6, ps] - 6;
b = Intersection[ps - 6, ps] + 6;
g = Graph[DeleteDuplicates[Thread[a \[UndirectedEdge] (a + 6)]~Join~Thread[(b - 6) \[UndirectedEdge] b]]];
sp = Sort /@ ConnectedComponents[g];
sp //= SortBy[First];
sp //= Map[AllSublengths];
sp //= Catenate;
sp //= SortBy[First];
sp //= DeleteDuplicates;
sel = Select[sp, Length /* EqualTo[2]];
Length[sel]
sel[[-5 ;;]] // Column
sel = Select[sp, Length /* EqualTo[3]];
Length[sel]
sel[[-5 ;;]] // Column
sel = Select[sp, Length /* EqualTo[4]];
Length[sel]
sel[[-5 ;;]] // Column
sel = Select[sp, Length /* EqualTo[5]];
Length[sel]
sel // Column
Select[Complement[primes, DeleteDuplicates[Catenate@sp]][[-20 ;;]], ! (PrimeQ[# + 6] \[Or] PrimeQ[# - 6]) &][[-10 ;;]] // Column

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Task/Sexy-primes/Nim/sexy-primes.nim Normal file
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import math, strformat, strutils
const Lim = 1_000_035
type Group {.pure.} = enum # "ord" gives the number of terms.
Unsexy = (1, "unsexy primes")
Pairs = (2, "sexy prime pairs")
Triplets = (3, "sexy prime triplets")
Quadruplets = (4, "sexy prime quadruplets")
Quintuplets = (5, "sexy prime quintuplets")
# Sieve of Erathosthenes.
var composite: array[1..Lim, bool] # Default is false.
composite[1] = true
for p in countup(3, sqrt(Lim.toFloat).int, 2): # Ignore even numbers.
if not composite[p]:
for k in countup(p * p, Lim, 2 * p):
composite[k] = true
template isPrime(n: int): bool = not composite[n]
proc expandGroup(n: int; group: Group): string =
## Given the first term of a group, return the full group
## representation as a string.
var n = n
for _ in 1..ord(group):
result.addSep(", ")
result.add $n
inc n, 6
if group != Unsexy: result = '(' & result & ')'
proc printResult(group: Group; values: seq[int]; count: int) =
## Print a result.
echo &"\nNumber of {group} less than {Lim}: {values.len}"
let last = min(values.len, count)
let verb = if last == 1: "is" else: "are"
echo &"The last {last} {verb}:"
var line = ""
for i in countdown(last, 1):
line.addSep(", ")
line.add expandGroup(values[^i], group)
echo " ", line
var
pairs, trips, quads, quints: seq[int] # Keep only the first prime of the group.
unsexy = @[2, 3]
for n in countup(3, Lim, 2):
if composite[n]: continue
if n in 7..(Lim - 8) and composite[n - 6] and composite[n + 6]:
unsexy.add n
continue
if n < Lim - 6 and isPrime(n + 6):
pairs.add n
else: continue
if n < Lim - 12 and isPrime(n + 12):
trips.add n
else: continue
if n < Lim - 18 and isPrime(n + 18):
quads.add n
else: continue
if n < Lim - 24 and isPrime(n + 24):
quints.add n
printResult(Pairs, pairs, 5)
printResult(Triplets, trips, 5)
printResult(Quadruplets, quads, 5)
printResult(Quintuplets, quints, 5)
printResult(Unsexy, unsexy, 10)

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Task/Sexy-primes/Pascal/sexy-primes.pas Normal file
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program SexyPrimes;
uses
SysUtils
{$IFNDEF FPC}
,windows // GettickCount64
{$ENDIF}
const
ctext: array[0..5] of string = ('Primes',
'sexy prime pairs',
'sexy prime triplets',
'sexy prime quadruplets',
'sexy prime quintuplet',
'sexy prime sextuplet');
primeLmt = 1000 * 1000 + 35;
type
sxPrtpl = record
spCnt,
splast5Idx: nativeInt;
splast5: array[0..6] of NativeInt;
end;
var
sieve: array[0..primeLmt] of byte;
sexyPrimesTpl: array[0..5] of sxPrtpl;
unsexyprimes: NativeUint;
procedure dosieve;
var
p, delPos, fact: NativeInt;
begin
p := 2;
repeat
if sieve[p] = 0 then
begin
delPos := primeLmt div p;
if delPos < p then
BREAK;
fact := delPos * p;
while delPos >= p do
begin
if sieve[delPos] = 0 then
sieve[fact] := 1;
Dec(delPos);
Dec(fact, p);
end;
end;
Inc(p);
until False;
end;
procedure CheckforSexy;
var
i, idx, sieveMask, tstMask: NativeInt;
begin
sieveMask := -1;
for i := 2 to primelmt do
begin
tstMask := 1;
sieveMask := sieveMask + sieveMask + sieve[i];
idx := 0;
repeat
if (tstMask and sieveMask) = 0 then
with sexyPrimesTpl[idx] do
begin
Inc(spCnt);
//memorize the last entry
Inc(splast5idx);
if splast5idx > 5 then
splast5idx := 1;
splast5[splast5idx] := i;
tstMask := tstMask shl 6 + 1;
end
else
begin
BREAK;
end;
Inc(idx);
until idx > 5;
end;
end;
procedure CheckforUnsexy;
var
i: NativeInt;
begin
for i := 2 to 6 do
begin
if (Sieve[i] = 0) and (Sieve[i + 6] = 1) then
Inc(unsexyprimes);
end;
for i := 2 + 6 to primelmt - 6 do
begin
if (Sieve[i] = 0) and (Sieve[i - 6] = 1) and (Sieve[i + 6] = 1) then
Inc(unsexyprimes);
end;
end;
procedure OutLast5(idx: NativeInt);
var
i, j, k: nativeInt;
begin
with sexyPrimesTpl[idx] do
begin
writeln(cText[idx], ' ', spCnt);
i := splast5idx + 1;
for j := 1 to 5 do
begin
if i > 5 then
i := 1;
if splast5[i] <> 0 then
begin
Write('[');
for k := idx downto 1 do
Write(splast5[i] - k * 6, ' ');
Write(splast5[i], ']');
end;
Inc(i);
end;
end;
writeln;
end;
procedure OutLastUnsexy(cnt:NativeInt);
var
i: NativeInt;
erg: array of NativeUint;
begin
if cnt < 1 then
EXIT;
setlength(erg,cnt);
dec(cnt);
if cnt < 0 then
EXIT;
for i := primelmt downto 2 + 6 do
begin
if (Sieve[i] = 0) and (Sieve[i - 6] = 1) and (Sieve[i + 6] = 1) then
Begin
erg[cnt] := i;
dec(cnt);
If cnt < 0 then
BREAK;
end;
end;
write('the last ',High(Erg)+1,' unsexy primes ');
For i := 0 to High(erg)-1 do
write(erg[i],',');
write(erg[High(erg)]);
end;
var
T1, T0: int64;
i: nativeInt;
begin
T0 := GettickCount64;
dosieve;
T1 := GettickCount64;
writeln('Sieving is done in ', T1 - T0, ' ms');
T0 := GettickCount64;
CheckforSexy;
T1 := GettickCount64;
writeln('Checking is done in ', T1 - T0, ' ms');
unsexyprimes := 0;
T0 := GettickCount64;
CheckforUnsexy;
T1 := GettickCount64;
writeln('Checking unsexy is done in ', T1 - T0, ' ms');
writeln('Limit : ', primelmt);
for i := 0 to 4 do
begin
OutLast5(i);
end;
writeln;
writeln(unsexyprimes,' unsexy primes');
OutLastUnsexy(10);
end.

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Task/Sexy-primes/Perl/sexy-primes-1.pl Normal file
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use ntheory qw/prime_iterator is_prime/;
sub tuple_tail {
my($n,$cnt,@array) = @_;
$n = @array if $n > @array;
my @tail;
for (1..$n) {
my $p = $array[-$n+$_-1];
push @tail, "(" . join(" ", map { $p+6*$_ } 0..$cnt-1) . ")";
}
return @tail;
}
sub comma {
(my $s = reverse shift) =~ s/(.{3})/$1,/g;
($s = reverse $s) =~ s/^,//;
return $s;
}
sub sexy_string { my $p = shift; is_prime($p+6) || is_prime($p-6) ? 'sexy' : 'unsexy' }
my $max = 1_000_035;
my $cmax = comma $max;
my $iter = prime_iterator;
my $p = $iter->();
my %primes;
push @{$primes{sexy_string($p)}}, $p;
while ( ($p = $iter->()) < $max) {
push @{$primes{sexy_string($p)}}, $p;
$p+ 6 < $max && is_prime($p+ 6) ? push @{$primes{'pair'}}, $p : next;
$p+12 < $max && is_prime($p+12) ? push @{$primes{'triplet'}}, $p : next;
$p+18 < $max && is_prime($p+18) ? push @{$primes{'quadruplet'}}, $p : next;
$p+24 < $max && is_prime($p+24) ? push @{$primes{'quintuplet'}}, $p : next;
}
print "Total primes less than $cmax: " . comma(@{$primes{'sexy'}} + @{$primes{'unsexy'}}) . "\n\n";
for (['pair', 2], ['triplet', 3], ['quadruplet', 4], ['quintuplet', 5]) {
my($sexy,$cnt) = @$_;
print "Number of sexy prime ${sexy}s less than $cmax: " . comma(scalar @{$primes{$sexy}}) . "\n";
print " Last 5 sexy prime ${sexy}s less than $cmax: " . join(' ', tuple_tail(5,$cnt,@{$primes{$sexy}})) . "\n";
print "\n";
}
print "Number of unsexy primes less than $cmax: ". comma(scalar @{$primes{unsexy}}) . "\n";
print " Last 10 unsexy primes less than $cmax: ". join(' ', @{$primes{unsexy}}[-10..-1]) . "\n";

18
Task/Sexy-primes/Perl/sexy-primes-2.pl Normal file
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use ntheory qw/sieve_prime_cluster forprimes is_prime/;
# ... identical helper functions
my %primes = (
sexy => [],
unsexy => [],
pair => [ sieve_prime_cluster(1, $max-1- 6, 6) ],
triplet => [ sieve_prime_cluster(1, $max-1-12, 6, 12) ],
quadruplet => [ sieve_prime_cluster(1, $max-1-18, 6, 12, 18) ],
quintuplet => [ sieve_prime_cluster(1, $max-1-24, 6, 12, 18, 24) ],
);
forprimes {
push @{$primes{sexy_string($_)}}, $_;
} $max-1;
# ... identical output code

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Task/Sexy-primes/Phix/sexy-primes.phix Normal file
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(phixonline)-->
<span style="color: #008080;">function</span> <span style="color: #000000;">create_sieve</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">limit</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">sieve</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #004600;">true</span><span style="color: #0000FF;">,</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">sieve</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">4</span> <span style="color: #008080;">to</span> <span style="color: #000000;">limit</span> <span style="color: #008080;">by</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">sieve</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">=</span><span style="color: #000000;">3</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">))</span> <span style="color: #008080;">by</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">p2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">*</span><span style="color: #000000;">p</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">sieve</span><span style="color: #0000FF;">[</span><span style="color: #000000;">p2</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">p2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">limit</span> <span style="color: #008080;">by</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">*</span><span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">sieve</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">sieve</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">lim</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1000035</span><span style="color: #0000FF;">,</span>
<span style="color: #000080;font-style:italic;">--constant lim = 100, -- (this works too)</span>
<span style="color: #000000;">limit</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">lim</span><span style="color: #0000FF;">-(</span><span style="color: #7060A8;">and_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lim</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">),</span> <span style="color: #000080;font-style:italic;">-- (limit must be odd)</span>
<span style="color: #000000;">sieve</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">create_sieve</span><span style="color: #0000FF;">(</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">+</span><span style="color: #000000;">6</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (+6 to check for sexiness)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">sets</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">({},</span><span style="color: #000000;">5</span><span style="color: #0000FF;">),</span> <span style="color: #000080;font-style:italic;">-- (unsexy,pairs,trips,quads,quins)</span>
<span style="color: #000000;">limits</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},</span>
<span style="color: #000000;">counts</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">&</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (2 is an unsexy prime)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">total</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span> <span style="color: #000080;font-style:italic;">-- ""</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">limit</span> <span style="color: #008080;">to</span> <span style="color: #000000;">3</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">2</span> <span style="color: #008080;">do</span> <span style="color: #000080;font-style:italic;">-- (this loop skips 2)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">sieve</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">total</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">sieve</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">6</span><span style="color: #0000FF;">]=</span><span style="color: #004600;">false</span> <span style="color: #008080;">and</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">-</span><span style="color: #000000;">6</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">or</span> <span style="color: #000000;">sieve</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">-</span><span style="color: #000000;">6</span><span style="color: #0000FF;">]=</span><span style="color: #004600;">false</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">counts</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span> <span style="color: #000080;font-style:italic;">-- unsexy</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sets</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])<</span><span style="color: #000000;">limits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">sets</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">prepend</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sets</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">else</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">set</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">i</span><span style="color: #0000FF;">-</span><span style="color: #000000;">6</span> <span style="color: #008080;">to</span> <span style="color: #000000;">3</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">6</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">j</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">0</span> <span style="color: #008080;">or</span> <span style="color: #000000;">sieve</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]=</span><span style="color: #004600;">false</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">set</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">prepend</span><span style="color: #0000FF;">(</span><span style="color: #000000;">set</span><span style="color: #0000FF;">,</span><span style="color: #000000;">j</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">set</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sets</span><span style="color: #0000FF;">[</span><span style="color: #000000;">l</span><span style="color: #0000FF;">])<</span><span style="color: #000000;">limits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">l</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">sets</span><span style="color: #0000FF;">[</span><span style="color: #000000;">l</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">prepend</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sets</span><span style="color: #0000FF;">[</span><span style="color: #000000;">l</span><span style="color: #0000FF;">],</span><span style="color: #000000;">set</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">counts</span><span style="color: #0000FF;">[</span><span style="color: #000000;">l</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sets</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])<</span><span style="color: #000000;">limits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">sets</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">prepend</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sets</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (as 2 skipped above)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">fmt</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"""
Of %,d primes less than %,d there are:
%,d unsexy primes, the last %d being %s
%,d pairs, the last %d being %s
%,d triplets, the last %d being %s
%,d quadruplets, the last %d being %s
%,d quintuplet, the last %d being %s
"""</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">results</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">total</span><span style="color: #0000FF;">,</span><span style="color: #000000;">lim</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #008000;">""</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #008000;">""</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #008000;">""</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #008000;">""</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #008000;">""</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">5</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">results</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">*</span><span style="color: #000000;">3</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">*</span><span style="color: #000000;">3</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">counts</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sets</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]),</span><span style="color: #7060A8;">sprint</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sets</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">results</span><span style="color: #0000FF;">)</span>
<!--

47
Task/Sexy-primes/Prolog/sexy-primes-1.pro Normal file
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sexy_prime_group(1, N, _, [N]):-
is_prime(N),
!.
sexy_prime_group(Size, N, Limit, [N|Group]):-
is_prime(N),
N1 is N + 6,
N1 =< Limit,
S1 is Size - 1,
sexy_prime_group(S1, N1, Limit, Group).
print_sexy_prime_groups(Size, Limit):-
findall(G, (is_prime(P), P =< Limit, sexy_prime_group(Size, P, Limit, G)), Groups),
length(Groups, Len),
writef('Number of groups of size %t is %t\n', [Size, Len]),
last_n(Groups, 5, Len, Last, Last_len),
writef('Last %t groups of size %t: %t\n\n', [Last_len, Size, Last]).
last_n([], _, L, [], L):-!.
last_n([_|List], Max, Length, Last, Last_len):-
Max < Length,
!,
Len1 is Length - 1,
last_n(List, Max, Len1, Last, Last_len).
last_n([E|List], Max, Length, [E|Last], Last_len):-
last_n(List, Max, Length, Last, Last_len).
unsexy(P):-
P1 is P + 6,
\+is_prime(P1),
P2 is P - 6,
\+is_prime(P2).
main(Limit):-
Max is Limit + 6,
find_prime_numbers(Max),
print_sexy_prime_groups(2, Limit),
print_sexy_prime_groups(3, Limit),
print_sexy_prime_groups(4, Limit),
print_sexy_prime_groups(5, Limit),
findall(P, (is_prime(P), P =< Limit, unsexy(P)), Unsexy),
length(Unsexy, Count),
writef('Number of unsexy primes is %t\n', [Count]),
last_n(Unsexy, 10, Count, Last10, _),
writef('Last 10 unsexy primes: %t', [Last10]).
main:-
main(1000035).

42
Task/Sexy-primes/Prolog/sexy-primes-2.pro Normal file
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:- module(prime_numbers, [find_prime_numbers/1, is_prime/1]).
:- dynamic is_prime/1.
find_prime_numbers(N):-
retractall(is_prime(_)),
assertz(is_prime(2)),
init_sieve(N, 3),
sieve(N, 3).
init_sieve(N, P):-
P > N,
!.
init_sieve(N, P):-
assertz(is_prime(P)),
Q is P + 2,
init_sieve(N, Q).
sieve(N, P):-
P * P > N,
!.
sieve(N, P):-
is_prime(P),
!,
S is P * P,
cross_out(S, N, P),
Q is P + 2,
sieve(N, Q).
sieve(N, P):-
Q is P + 2,
sieve(N, Q).
cross_out(S, N, _):-
S > N,
!.
cross_out(S, N, P):-
retract(is_prime(S)),
!,
Q is S + 2 * P,
cross_out(Q, N, P).
cross_out(S, N, P):-
Q is S + 2 * P,
cross_out(Q, N, P).

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Task/Sexy-primes/PureBasic/sexy-primes.basic Normal file
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DisableDebugger
EnableExplicit
#LIM=1000035
Macro six(mul)
6*mul
EndMacro
Macro form(n)
RSet(Str(n),8)
EndMacro
Macro put(m,g,n)
PrintN(Str(m)+" "+g)
PrintN(n)
EndMacro
Define c1.i=2,c2.i,c3.i,c4.i,c5.i,t1$,t2$,t3$,t4$,t5$,i.i,j.i
Global Dim soe.b(#LIM)
FillMemory(@soe(0),#LIM,#True,#PB_Byte)
If Not OpenConsole("")
End 1
EndIf
For i=2 To Sqr(#LIM)
If soe(i)=#True
j=i*i
While j<=#LIM
soe(j)=#False
j+i
Wend
EndIf
Next
Procedure.s formtab(t$,l.i)
If CountString(t$,~"\n")>l
t$=Mid(t$,FindString(t$,~"\n")+1)
EndIf
ProcedureReturn t$
EndProcedure
For i=3 To #LIM Step 2
If i>5 And i<#LIM-6 And soe(i)&~(soe(i-six(1))|soe(i+six(1)))
c1+1
t1$+form(i)+~"\n"
t1$=formtab(t1$,10)
Continue
EndIf
If i<#LIM-six(1) And soe(i)&soe(i+six(1))
c2+1
t2$+form(i)+form(i+six(1))+~"\n"
t2$=formtab(t2$,5)
EndIf
If i<#LIM-six(2) And soe(i)&soe(i+six(1))&soe(i+six(2))
c3+1
t3$+form(i)+form(i+six(1))+form(i+six(2))+~"\n"
t3$=formtab(t3$,5)
EndIf
If i<#LIM-six(3) And soe(i)&soe(i+six(1))&soe(i+six(2))&soe(i+six(3))
c4+1
t4$+form(i)+form(i+six(1))+form(i+six(2))+form(i+six(3))+~"\n"
t4$=formtab(t4$,5)
EndIf
If i<#LIM-six(4) And soe(i)&soe(i+six(1))&soe(i+six(2))&soe(i+six(3))&soe(i+six(4))
c5+1
t5$+form(i)+form(i+six(1))+form(i+six(2))+form(i+six(3))+form(i+six(4))+~"\n"
t5$=formtab(t5$,5)
EndIf
Next
put(c2,"pairs ending with ...",t2$)
put(c3,"triplets ending with ...",t3$)
put(c4,"quadruplets ending with ...",t4$)
put(c5,"quintuplets ending with ...",t5$)
put(c1,"unsexy primes ending with ...",t1$)
Input()

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Task/Sexy-primes/Python/sexy-primes-1.py Normal file
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LIMIT = 1_000_035
def primes2(limit=LIMIT):
if limit < 2: return []
if limit < 3: return [2]
lmtbf = (limit - 3) // 2
buf = [True] * (lmtbf + 1)
for i in range((int(limit ** 0.5) - 3) // 2 + 1):
if buf[i]:
p = i + i + 3
s = p * (i + 1) + i
buf[s::p] = [False] * ((lmtbf - s) // p + 1)
return [2] + [i + i + 3 for i, v in enumerate(buf) if v]
primes = primes2(LIMIT +6)
primeset = set(primes)
primearray = [n in primeset for n in range(LIMIT)]
#%%
s = [[] for x in range(4)]
unsexy = []
for p in primes:
if p > LIMIT:
break
if p + 6 in primeset and p + 6 < LIMIT:
s[0].append((p, p+6))
elif p + 6 in primeset:
break
else:
if p - 6 not in primeset:
unsexy.append(p)
continue
if p + 12 in primeset and p + 12 < LIMIT:
s[1].append((p, p+6, p+12))
else:
continue
if p + 18 in primeset and p + 18 < LIMIT:
s[2].append((p, p+6, p+12, p+18))
else:
continue
if p + 24 in primeset and p + 24 < LIMIT:
s[3].append((p, p+6, p+12, p+18, p+24))
#%%
print('"SEXY" PRIME GROUPINGS:')
for sexy, name in zip(s, 'pairs triplets quadruplets quintuplets'.split()):
print(f' {len(sexy)} {na (not isPrime(n-6))))) |> Array.ofSeq
printfn "There are %d unsexy primes less than 1,000,035. The last 10 are:" n.Length
Array.skip (n.Length-10) n |> Array.iter(fun n->printf "%d " n); printfn ""
let ni=pCache |> Seq.takeWhile(fun n->nme} ending with ...')
for sx in sexy[-5:]:
print(' ',sx)
print(f'\nThere are {len(unsexy)} unsexy primes ending with ...')
for usx in unsexy[-10:]:
print(' ',usx)

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Task/Sexy-primes/Python/sexy-primes-2.py Normal file
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#Functional Sexy Primes. Nigel Galloway: October 5th., 2018
from itertools import *
z=primes()
n=frozenset(takewhile(lambda x: x<1000035,z))
ni=sorted(list(filter(lambda g: n.__contains__(g+6) ,n)))
print ("There are",len(ni),"sexy prime pairs all components of which are less than 1,000,035. The last 5 are:")
for g in islice(ni,max(len(ni)-5,0),len(ni)): print(format("(%d,%d) " % (g,g+6)))
nig=list(filter(lambda g: n.__contains__(g+12) ,ni))
print ("There are",len(nig),"sexy prime triplets all components of which are less than 1,000,035. The last 5 are:")
for g in islice(nig,max(len(nig)-5,0),len(nig)): print(format("(%d,%d,%d) " % (g,g+6,g+12)))
nige=list(filter(lambda g: n.__contains__(g+18) ,nig))
print ("There are",len(nige),"sexy prime quadruplets all components of which are less than 1,000,035. The last 5 are:")
for g in islice(nige,max(len(nige)-5,0),len(nige)): print(format("(%d,%d,%d,%d) " % (g,g+6,g+12,g+18)))
nigel=list(filter(lambda g: n.__contains__(g+24) ,nige))
print ("There are",len(nigel),"sexy prime quintuplets all components of which are less than 1,000,035. The last 5 are:")
for g in islice(nigel,max(len(nigel)-5,0),len(nigel)): print(format("(%d,%d,%d,%d,%d) " % (g,g+6,g+12,g+18,g+24)))
un=frozenset(takewhile(lambda x: x<1000050,z)).union(n)
unsexy=sorted(list(filter(lambda g: not un.__contains__(g+6) and not un.__contains__(g-6),n)))
print ("There are",len(unsexy),"unsexy primes less than 1,000,035. The last 10 are:")
for g in islice(unsexy,max(len(unsexy)-10,0),len(unsexy)): print(g)

36
Task/Sexy-primes/Quackery/sexy-primes.quackery Normal file
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1000035 eratosthenes
[ stack ] is pairs ( --> s )
[ stack ] is trips ( --> s )
[ stack ] is quads ( --> s )
[ stack ] is quins ( --> s )
[ stack ] is unsexy ( --> s )
[ share swap bit & 0 != ] is in ( s n --> b )
primes share dup
' [ pairs trips quads quins ]
witheach
[ dip [ dip dup 6 >> & dup ] put ]
2drop
pairs share
dup 6 << | ~
primes share &
unsexy put
' [ pairs trips quads quins ]
witheach
[ temp put
[] 1000035 times
[ i^ temp share in if
[ i^ join ] ]
dup size echo sp
-5 split echo drop cr
temp release ]
cr
[] 1000035 6 - times
[ i^ unsexy in if
[ i^ join ] ]
dup size echo sp
-10 split echo drop cr

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Task/Sexy-primes/REXX/sexy-primes.rexx Normal file
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/*REXX program finds and displays various kinds of sexy and unsexy primes less than N.*/
parse arg N endU end2 end3 end4 end5 . /*obtain optional argument from the CL.*/
if N=='' | N=="," then N= 1000035 - 1 /*Not specified? Then use the default.*/
if endU=='' | endU=="," then endU= 10 /* " " " " " " */
if end2=='' | end2=="," then end2= 5 /* " " " " " " */
if end3=='' | end3=="," then end3= 5 /* " " " " " " */
if end4=='' | end4=="," then end4= 5 /* " " " " " " */
if end5=='' | end5=="," then end4= 5 /* " " " " " " */
call genSq /*gen some squares for the DO k=7 UNTIL*/
call genPx /* " prime (@.) & sexy prime (X.) array*/
call genXU /*gen lists, types of sexy Ps, unsexy P*/
call getXs /*gen lists, last # of types of sexy Ps*/
@sexy= ' sexy prime' /*a handy literal for some of the SAYs.*/
w2= words( translate(x2,, '~') ); y2= words(x2) /*count #primes in the sexy pairs. */
w3= words( translate(x3,, '~') ); y3= words(x3) /* " " " " " " triplets. */
w4= words( translate(x4,, '~') ); y4= words(x4) /* " " " " " " quadruplets*/
w5= words( translate(x5,, '~') ); y5= words(x5) /* " " " " " " quintuplets*/
say 'There are ' commas(w2%2) @sexy "pairs less than " Nc
say 'The last ' commas(end2) @sexy "pairs are:"; say subword(x2, max(1,y2-end2+1))
say
say 'There are ' commas(w3%3) @sexy "triplets less than " Nc
say 'The last ' commas(end3) @sexy "triplets are:"; say subword(x3, max(1,y3-end3+1))
say
say 'There are ' commas(w4%4) @sexy "quadruplets less than " Nc
say 'The last ' commas(end4) @sexy "quadruplets are:"; say subword(x4, max(1,y4-end4+1))
say
say 'There is ' commas(w5%5) @sexy "quintuplet less than " Nc
say 'The last ' commas(end4) @sexy "quintuplet are:"; say subword(x5, max(1,y5-end4+1))
say
say 'There are ' commas(s1) " sexy primes less than " Nc
say 'There are ' commas(u1) " unsexy primes less than " Nc
say 'The last ' commas(endU) " unsexy primes are: " subword(u, max(1,u1-endU+1))
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
commas: procedure; parse arg _; n= _'.9'; #= 123456789; b= verify(n, #, "M")
e= verify(n, #'0', , verify(n, #"0.", 'M') ) - 4
do j=e to b by -3; _= insert(',', _, j); end /*j*/; return _
/*──────────────────────────────────────────────────────────────────────────────────────*/
genSQ: do i=17 by 2 until i**2 > N+7; s.i= i**2; end; return /*S used for square roots*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
genPx: @.=; #= 0; !.= 0. /*P array; P count; sexy P array*/
if N>1 then do; #= 1; @.1= 2; !.2= 1; end /*count of primes found (so far)*/
x.=!.; LPs=3 5 7 11 13 17 /*sexy prime array; low P list.*/
do j=3 by 2 to N+6 /*start in the cellar & work up.*/
if j<19 then if wordpos(j, LPs)==0 then iterate
else do; #= #+1; @.#= j; !.j= 1; b= j - 6
if !.b then x.b= 1; iterate
end
if j// 3 ==0 then iterate /* ··· and eliminate multiples of 3.*/
parse var j '' -1 _ /* get the rightmost digit of J. */
if _ ==5 then iterate /* ··· and eliminate multiples of 5.*/
if j// 7 ==0 then iterate /* ··· " " " " 7.*/
if j//11 ==0 then iterate /* ··· " " " " 11.*/
if j//13 ==0 then iterate /* ··· " " " " 13.*/
do k=7 until s._ > j; _= @.k /*÷ by primes starting at 7th prime. */
if j // _ == 0 then iterate j /*get the remainder of j÷@.k ___ */
end /*k*/ /*divide up through & including √ J */
if j<=N then do; #= #+1; @.#= j; end /*bump P counter; assign prime to @.*/
!.j= 1 /*define Jth number as being prime.*/
b= j - 6 /*B: lower part of a sexy prime pair?*/
if !.b then do; x.b=1; if j<=N then x.j=1; end /*assign (both parts ?) sexy Ps.*/
end /*j*/; return
/*──────────────────────────────────────────────────────────────────────────────────────*/
genXU: u= 2; Nc=commas(N+1); s= /*1st unsexy prime; add commas to N+1*/
say 'There are ' commas(#) " primes less than " Nc; say
do k=2 for #-1; p= @.k; if x.p then s=s p /*if sexy prime, add it to list*/
else u= u p /* " unsexy " " " " " */
end /*k*/ /* [↑] traispe through odd Ps. */
s1= words(s); u1= words(u); return /*# of sexy primes; # unsexy primes.*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
getXs: x2=; do k=2 for #-1; p=@.k; if \x.p then iterate /*build sexy prime list. */
b=p- 6; if \x.b then iterate; x2=x2 b'~'p
end /*k*/
x3=; do k=2 for #-1; p=@.k; if \x.p then iterate /*build sexy P triplets. */
b=p- 6; if \x.b then iterate
t=p-12; if \x.t then iterate; x3=x3 t'~' || b"~"p
end /*k*/
x4=; do k=2 for #-1; p=@.k; if \x.p then iterate /*build sexy P quads. */
b=p- 6; if \x.b then iterate
t=p-12; if \x.t then iterate
q=p-18; if \x.q then iterate; x4=x4 q'~'t"~" || b'~'p
end /*k*/
x5=; do k=2 for #-1; p=@.k; if \x.p then iterate /*build sexy P quints. */
b=p- 6; if \x.b then iterate
t=p-12; if \x.t then iterate
q=p-18; if \x.q then iterate
v=p-24; if \x.v then iterate; x5=x5 v'~'q"~"t'~' || b"~"p
end /*k*/; return

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Task/Sexy-primes/Raku/sexy-primes.raku Normal file
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use Math::Primesieve;
my $sieve = Math::Primesieve.new;
my $max = 1_000_035;
my @primes = $sieve.primes($max);
my $filter = @primes.Set;
my $primes = @primes.categorize: &sexy;
say "Total primes less than {comma $max}: ", comma +@primes;
for <pair 2 triplet 3 quadruplet 4 quintuplet 5> -> $sexy, $cnt {
say "Number of sexy prime {$sexy}s less than {comma $max}: ", comma +$primes{$sexy};
say " Last 5 sexy prime {$sexy}s less than {comma $max}: ",
join ' ', $primes{$sexy}.tail(5).grep(*.defined).map:
{ "({ $_ «+« (0,6 … 24)[^$cnt] })" }
say '';
}
say "Number of unsexy primes less than {comma $max}: ", comma +$primes<unsexy>;
say " Last 10 unsexy primes less than {comma $max}: ", $primes<unsexy>.tail(10);
sub sexy ($i) {
gather {
take 'quintuplet' if all($filter{$i «+« (6,12,18,24)});
take 'quadruplet' if all($filter{$i «+« (6,12,18)});
take 'triplet' if all($filter{$i «+« (6,12)});
take 'pair' if $filter{$i + 6};
take (($i >= $max - 6) && ($i + 6).is-prime) ||
(so any($filter{$i «+« (6, -6)})) ?? 'sexy' !! 'unsexy';
}
}
sub comma { $^i.flip.comb(3).join(',').flip }

72
Task/Sexy-primes/Ring/sexy-primes.ring Normal file
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load "stdlib.ring"
primes = []
for n = 1 to 100
if isprime(n)
add(primes,n)
ok
next
see "Sexy prime pairs under 100:" + nl + nl
for n = 1 to len(primes)-1
for m = n + 1 to len(primes)
if primes[m] - primes[n] = 6
see "(" + primes[n] + " " + primes[m] + ")" + nl
ok
next
next
see nl
see "Sexy prime triplets under 100:" + nl +nl
for n = 1 to len(primes)-2
for m = n + 1 to len(primes)-1
for x = m + 1 to len(primes)
bool1 = (primes[m] - primes[n] = 6)
bool2 = (primes[x] - primes[m] = 6)
bool = bool1 and bool2
if bool
see "(" + primes[n] + " " + primes[m] + " " + primes[x] + ")" + nl
ok
next
next
next
see nl
see "Sexy prime quadruplets under 100:" + nl + nl
for n = 1 to len(primes)-3
for m = n + 1 to len(primes)-2
for x = m + 1 to len(primes)-1
for y = m + 1 to len(primes)
bool1 = (primes[m] - primes[n] = 6)
bool2 = (primes[x] - primes[m] = 6)
bool3 = (primes[y] - primes[x] = 6)
bool = bool1 and bool2 and bool3
if bool
see "(" + primes[n] + " " + primes[m] + " " + primes[x] + " " + primes[y] + ")" + nl
ok
next
next
next
next
see nl
see "Sexy prime quintuplets under 100:" + nl + nl
for n = 1 to len(primes)-4
for m = n + 1 to len(primes)-3
for x = m + 1 to len(primes)-2
for y = m + 1 to len(primes)-1
for z = y + 1 to len(primes)
bool1 = (primes[m] - primes[n] = 6)
bool2 = (primes[x] - primes[m] = 6)
bool3 = (primes[y] - primes[x] = 6)
bool4 = (primes[z] - primes[y] = 6)
bool = bool1 and bool2 and bool3 and bool4
if bool
see "(" + primes[n] + " " + primes[m] + " " + primes[x] + " " +
primes[y] + " " + primes[z] + ")" + nl
ok
next
next
next
next
next

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Task/Sexy-primes/Ruby/sexy-primes.rb Normal file
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require 'prime'
prime_array, sppair2, sppair3, sppair4, sppair5 = Array.new(5) {Array.new()} # arrays for prime numbers and index number to array for each pair.
unsexy, i, start = [2], 0, Time.now
Prime.each(1_000_100) {|prime| prime_array.push prime}
while prime_array[i] < 1_000_035
i+=1
unsexy.push(i) if prime_array[(i+1)..(i+2)].include?(prime_array[i]+6) == false && prime_array[(i-2)..(i-1)].include?(prime_array[i]-6) == false && prime_array[i]+6 < 1_000_035
prime_array[(i+1)..(i+4)].include?(prime_array[i]+6) && prime_array[i]+6 < 1_000_035 ? sppair2.push(i) : next
prime_array[(i+2)..(i+5)].include?(prime_array[i]+12) && prime_array[i]+12 < 1_000_035 ? sppair3.push(i) : next
prime_array[(i+3)..(i+6)].include?(prime_array[i]+18) && prime_array[i]+18 < 1_000_035 ? sppair4.push(i) : next
prime_array[(i+4)..(i+7)].include?(prime_array[i]+24) && prime_array[i]+24 < 1_000_035 ? sppair5.push(i) : next
end
puts "\nSexy prime pairs: #{sppair2.size} found:"
sppair2.last(5).each {|prime| print [prime_array[prime], prime_array[prime]+6].join(" - "), "\n"}
puts "\nSexy prime triplets: #{sppair3.size} found:"
sppair3.last(5).each {|prime| print [prime_array[prime], prime_array[prime]+6, prime_array[prime]+12].join(" - "), "\n"}
puts "\nSexy prime quadruplets: #{sppair4.size} found:"
sppair4.last(5).each {|prime| print [prime_array[prime], prime_array[prime]+6, prime_array[prime]+12, prime_array[prime]+18].join(" - "), "\n"}
puts "\nSexy prime quintuplets: #{sppair5.size} found:"
sppair5.last(5).each {|prime| print [prime_array[prime], prime_array[prime]+6, prime_array[prime]+12, prime_array[prime]+18, prime_array[prime]+24].join(" - "), "\n"}
puts "\nUnSexy prime: #{unsexy.size} found. Last 10 are:"
unsexy.last(10).each {|item| print prime_array[item], " "}
print "\n\n", Time.now - start, " seconds"

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Task/Sexy-primes/Rust/sexy-primes.rust Normal file
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// [dependencies]
// primal = "0.2"
// circular-queue = "0.2.5"
use circular_queue::CircularQueue;
fn main() {
let max = 1000035;
let max_group_size = 5;
let diff = 6;
let max_groups = 5;
let max_unsexy = 10;
let sieve = primal::Sieve::new(max + diff);
let mut group_count = vec![0; max_group_size];
let mut unsexy_count = 0;
let mut groups = Vec::new();
let mut unsexy_primes = CircularQueue::with_capacity(max_unsexy);
for _ in 0..max_group_size {
groups.push(CircularQueue::with_capacity(max_groups));
}
for p in sieve.primes_from(2).take_while(|x| *x < max) {
if !sieve.is_prime(p + diff) && (p < diff + 2 || !sieve.is_prime(p - diff)) {
unsexy_count += 1;
unsexy_primes.push(p);
} else {
let mut group = Vec::new();
group.push(p);
for group_size in 1..max_group_size {
let next = p + group_size * diff;
if next >= max || !sieve.is_prime(next) {
break;
}
group.push(next);
group_count[group_size] += 1;
groups[group_size].push(group.clone());
}
}
}
for size in 1..max_group_size {
println!(
"Number of groups of size {} is {}",
size + 1,
group_count[size]
);
println!("Last {} groups of size {}:", groups[size].len(), size + 1);
println!(
"{}\n",
groups[size]
.asc_iter()
.map(|g| format!("({})", to_string(&mut g.iter())))
.collect::<Vec<String>>()
.join(", ")
);
}
println!("Number of unsexy primes is {}", unsexy_count);
println!("Last {} unsexy primes:", unsexy_primes.len());
println!("{}", to_string(&mut unsexy_primes.asc_iter()));
}
fn to_string<T: ToString>(iter: &mut dyn std::iter::Iterator<Item = T>) -> String {
iter.map(|n| n.to_string())
.collect::<Vec<String>>()
.join(", ")
}

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Task/Sexy-primes/Scala/sexy-primes.scala Normal file
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/* We could reduce the number of functions through a polymorphism since we're trying to retrieve sexy N-tuples (pairs, triplets etc...)
but one practical solution would be to use the Shapeless library for this purpose; here we only use built-in Scala packages. */
object SexyPrimes {
/** Check if an input number is prime or not*/
def isPrime(n: Int): Boolean = ! ((2 until n-1) exists (n % _ == 0)) && n > 1
/** Retrieve pairs of sexy primes given a list of Integers*/
def getSexyPrimesPairs (primes : List[Int]) = {
primes
.map(n => if(primes.contains(n+6)) (n, n+6))
.filter(p => p != ())
.map{ case (a,b) => (a.toString.toInt, b.toString.toInt)}
}
/** Retrieve triplets of sexy primes given a list of Integers*/
def getSexyPrimesTriplets (primes : List[Int]) = {
primes
.map(n => if(
primes.contains(n+6) && primes.contains(n+12))
(n, n+6, n+12)
)
.filter(p => p != ())
.map{ case (a,b,c) => (a.toString.toInt, b.toString.toInt, c.toString.toInt)}
}
/** Retrieve quadruplets of sexy primes given a list of Integers*/
def getSexyPrimesQuadruplets (primes : List[Int]) = {
primes
.map(n => if(
primes.contains(n+6) && primes.contains(n+12) && primes.contains(n+18))
(n, n+6, n+12, n+18)
)
.filter(p => p != ())
.map{ case (a,b,c,d) => (a.toString.toInt, b.toString.toInt, c.toString.toInt, d.toString.toInt)}
}
/** Retrieve quintuplets of sexy primes given a list of Integers*/
def getSexyPrimesQuintuplets (primes : List[Int]) = {
primes
.map(n => if (
primes.contains(n+6) && primes.contains(n+12) && primes.contains(n+18) && primes.contains(n + 24))
(n, n + 6, n + 12, n + 18, n + 24)
)
.filter(p => p != ())
.map { case (a, b, c, d, e) => (a.toString.toInt, b.toString.toInt, c.toString.toInt, d.toString.toInt, e.toString.toInt) }
}
/** Retrieve all unsexy primes between 1 and a given limit from an input list of Integers*/
def removeOutsideSexyPrimes( l : List[Int], limit : Int) : List[Int] = {
l.filter(n => !isPrime(n+6) && n+6 < limit)
}
def main(args: Array[String]): Unit = {
val limit = 1000035
val l = List.range(1,limit)
val primes = l.filter( n => isPrime(n))
val sexyPairs = getSexyPrimesPairs(primes)
println("Number of sexy pairs : " + sexyPairs.size)
println("5 last sexy pairs : " + sexyPairs.takeRight(5))
val primes2 = sexyPairs.flatMap(t => List(t._1, t._2)).distinct.sorted
val sexyTriplets = getSexyPrimesTriplets(primes2)
println("Number of sexy triplets : " + sexyTriplets.size)
println("5 last sexy triplets : " + sexyTriplets.takeRight(5))
val primes3 = sexyTriplets.flatMap(t => List(t._1, t._2, t._3)).distinct.sorted
val sexyQuadruplets = getSexyPrimesQuadruplets(primes3)
println("Number of sexy quadruplets : " + sexyQuadruplets.size)
println("5 last sexy quadruplets : " + sexyQuadruplets.takeRight(5))
val primes4 = sexyQuadruplets.flatMap(t => List(t._1, t._2, t._3, t._4)).distinct.sorted
val sexyQuintuplets = getSexyPrimesQuintuplets(primes4)
println("Number of sexy quintuplets : " + sexyQuintuplets.size)
println("The last sexy quintuplet : " + sexyQuintuplets.takeRight(10))
val sexyPrimes = primes2.toSet
val unsexyPrimes = removeOutsideSexyPrimes( primes.toSet.diff((sexyPrimes)).toList.sorted, limit)
println("Number of unsexy primes : " + unsexyPrimes.size)
println("10 last unsexy primes : " + unsexyPrimes.takeRight(10))
}
}

22
Task/Sexy-primes/Sidef/sexy-primes.sidef Normal file
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var limit = 1e6+35
var primes = limit.primes
say "Total number of primes <= #{limit.commify} is #{primes.len.commify}."
say "Sexy k-tuple primes <= #{limit.commify}:\n"
(2..5).each {|k|
var groups = []
primes.each {|p|
var group = (1..^k -> map {|j| 6*j + p })
if (group.all{.is_prime} && (group[-1] <= limit)) {
groups << [p, group...]
}
}
say "...total number of sexy #{k}-tuple primes = #{groups.len.commify}"
say "...where last 5 tuples are: #{groups.last(5).map{'('+.join(' ')+')'}.join(' ')}\n"
}
var unsexy_primes = primes.grep {|p| is_prime(p+6) || is_prime(p-6) -> not }
say "...total number of unsexy primes = #{unsexy_primes.len.commify}"
say "...where last 10 unsexy primes are: #{unsexy_primes.last(10)}"

63
Task/Sexy-primes/Wren/sexy-primes.wren Normal file
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import "/fmt" for Fmt
import "/math" for Int
var printHelper = Fn.new { |cat, le, lim, max|
var cle = Fmt.commatize(le)
var clim = Fmt.commatize(lim)
if (cat != "unsexy primes") cat = "sexy prime " + cat
System.print("Number of %(cat) less than %(clim) = %(cle)")
var last = (le < max) ? le : max
var verb = (last == 1) ? "is" : "are"
return [le, last, verb]
}
var lim = 1000035
var sv = Int.primeSieve(lim-1, false)
var pairs = []
var trips = []
var quads = []
var quins = []
var unsexy = [2, 3]
var i = 3
while (i < lim) {
if (i > 5 && i < lim-6 && !sv[i] && sv[i-6] && sv[i+6]) {
unsexy.add(i)
} else {
if (i < lim-6 && !sv[i] && !sv[i+6]) {
pairs.add([i, i+6])
if (i < lim-12 && !sv[i+12]) {
trips.add([i, i+6, i+12])
if (i < lim-18 && !sv[i+18]) {
quads.add([i, i+6, i+12, i+18])
if (i < lim-24 && !sv[i+24]) {
quins.add([i, i+6, i+12, i+18, i+24])
}
}
}
}
}
i = i + 2
}
var le
var n
var verb
var unwrap = Fn.new { |t|
le = t[0]
n = t[1]
verb = t[2]
}
unwrap.call(printHelper.call("pairs", pairs.count, lim, 5))
System.print("The last %(n) %(verb):\n %(pairs[le-n..-1])\n")
unwrap.call(printHelper.call("triplets", trips.count, lim, 5))
System.print("The last %(n) %(verb):\n %(trips[le-n..-1])\n")
unwrap.call(printHelper.call("quadruplets", quads.count, lim, 5))
System.print("The last %(n) %(verb):\n %(quads[le-n..-1])\n")
unwrap.call(printHelper.call("quintuplets", quins.count, lim, 5))
System.print("The last %(n) %(verb):\n %(quins[le-n..-1])\n")
unwrap.call(printHelper.call("unsexy primes", unsexy.count, lim, 10))
System.print("The last %(n) %(verb):\n %(unsexy[le-n..-1])\n")

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Task/Sexy-primes/XPL0/sexy-primes.xpl0 Normal file
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func IsPrime(N); \Return 'true' if N is prime
int N, I;
[if N <= 2 then return N = 2;
if (N&1) = 0 then \even >2\ return false;
for I:= 3 to sqrt(N) do
[if rem(N/I) = 0 then return false;
I:= I+1;
];
return true;
];
int CU, C2, C3, C4, C5, N, I;
int Unsexy(10), Pairs(5), Trips(5), Quads(5), Quins(5);
[CU:= 0; C2:= 0; C3:= 0; C4:= 0; C5:= 0;
for N:= 1000035 downto 2 do
[if IsPrime(N) then
[if IsPrime(N-6) then
[if C2 < 5 then Pairs(C2):= N;
C2:= C2+1;
if IsPrime(N-12) then
[if C3 < 5 then Trips(C3):= N;
C3:= C3+1;
if IsPrime(N-18) then
[if C4 < 5 then Quads(C4):= N;
C4:= C4+1;
if IsPrime(N-24) then
[if C5 < 5 then Quins(C5):= N;
C5:= C5+1;
];
];
];
]
else if not IsPrime(N+6) then
[if CU < 10 then Unsexy(CU):= N;
CU:= CU+1;
];
];
];
IntOut(0, C2); Text(0, " pairs ending with:^m^j");
for I:= 4 downto 0 do
[Text(0, " [");
IntOut(0, Pairs(I)-6); Text(0, ", ");
IntOut(0, Pairs(I)); Text(0, "]^m^j");
];
IntOut(0, C3); Text(0, " triplets ending with:^m^j");
for I:= 4 downto 0 do
[Text(0, " [");
IntOut(0, Trips(I)-12); Text(0, ", ");
IntOut(0, Trips(I)-6); Text(0, ", ");
IntOut(0, Trips(I)); Text(0, "]^m^j");
];
IntOut(0, C4); Text(0, " quadruplets ending with:^m^j");
for I:= 4 downto 0 do
[Text(0, " [");
IntOut(0, Quads(I)-18); Text(0, ", ");
IntOut(0, Quads(I)-12); Text(0, ", ");
IntOut(0, Quads(I)-6); Text(0, ", ");
IntOut(0, Quads(I)); Text(0, "]^m^j");
];
IntOut(0, C5); Text(0, " quintuplet(s) ending with:^m^j");
I:= if C5 > 5 then 5 else C5;
for I:= I-1 downto 0 do
[Text(0, " [");
IntOut(0, Quins(I)-24); Text(0, ", ");
IntOut(0, Quins(I)-18); Text(0, ", ");
IntOut(0, Quins(I)-12); Text(0, ", ");
IntOut(0, Quins(I)-6); Text(0, ", ");
IntOut(0, Quins(I)); Text(0, "]^m^j");
];
IntOut(0, CU); Text(0, " unsexy primes ending with:^m^j");
for I:= 9 downto 0 do
[IntOut(0, Unsexy(I)); if I then Text(0, ", ")];
CrLf(0);
]

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Task/Sexy-primes/Zkl/sexy-primes.zkl Normal file
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var [const] BI=Import("zklBigNum"); // libGMP
const N=1_000_035, M=N+24; // M allows prime group to span N, eg N=100, (97,103)
const OVR=6; // 6 if prime group can NOT span N, else 0
ps,p := Data(M+50).fill(0), BI(1); // slop at the end (for reverse wrap around)
while(p.nextPrime()<=M){ ps[p]=1 } // bitmap of primes
ns:=(N-OVR).filter('wrap(n){ 2==(ps[n] + ps[n+6]) }); # know 2 isn't, check anyway
msg(N,"sexy prime pairs",ns,5,1);
ns:=[3..N-(6+OVR),2].filter('wrap(n){ 3==(ps[n] + ps[n+6] + ps[n+12]) }); # can't be even
msg(N,"sexy triplet primes",ns,5,2);
ns:=[3..N-(12+OVR),2].filter('wrap(n){ 4==(ps[n] + ps[n+6] + ps[n+12] + ps[n+18]) }); # no evens
msg(N,"sexy quadruplet primes",ns,5,3);
ns:=[3..N-(18+OVR),2].filter('wrap(n){ 5==(ps[n] + ps[n+6] + ps[n+12] + ps[n+18] + ps[n+24]) });
msg(N,"sexy quintuplet primes",ns,1,4);
ns:=(N-OVR).filter('wrap(n){ ps[n] and 0==(ps[n-6] + ps[n+6]) }); // include 2
msg(N,"unsexy primes",ns,10,0);
fcn msg(N,s,ps,n,g){
n=n.min(ps.len()); // if the number of primes is less than n
gs:=ps[-n,*].apply('wrap(n){ [0..g*6,6].apply('+(n)) })
.pump(String,T("concat", ","),"(%s) ".fmt);
println("Number of %s less than %,d is %,d".fmt(s,N,ps.len()));
println("The last %d %s:\n %s\n".fmt(n, (n>1 and "are" or "is"), gs));
}