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Ingy döt Net 2023-07-01 11:58:00 -04:00
parent 7387c8f97b
commit cb5bb5e222
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3
Task/Cuban-primes/00-META.yaml Normal file
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---
from: http://rosettacode.org/wiki/Cuban_primes
note: Prime Numbers

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Task/Cuban-primes/00-TASK.txt Normal file
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The name   '''cuban'''   has nothing to do with   [https://en.wikipedia.org/wiki/Cuba Cuba  (the country)],   but has to do with the
fact that cubes &nbsp; (3<sup>rd</sup> powers) &nbsp; play a role in its definition.
;Some definitions of cuban primes:
::* &nbsp; primes which are the difference of two consecutive cubes.
::* &nbsp; primes of the form: &nbsp; (n+1)<sup>3</sup> - n<sup>3</sup>.
::* &nbsp; primes of the form: &nbsp; n<sup>3</sup> - (n-1)<sup>3</sup>.
::* &nbsp; primes &nbsp; ''p'' &nbsp; such that &nbsp; n<sup>2</sup>(''p''+n) &nbsp; is a cube for some &nbsp; n>0.
::* &nbsp; primes &nbsp; ''p'' &nbsp; such that &nbsp; 4''p'' = 1 + 3n<sup>2</sup>.
Cuban primes were named in 1923 by Allan Joseph Champneys Cunningham.
;Task requirements:
::* &nbsp; show the first &nbsp; 200 &nbsp; cuban primes &nbsp; (in a multi─line horizontal format).
::* &nbsp; show the &nbsp; 100,000<sup>th</sup> &nbsp; cuban prime.
::* &nbsp; show all cuban primes with commas &nbsp; (if appropriate).
::* &nbsp; show all output here.
Note that &nbsp; '''cuban prime''' &nbsp; isn't capitalized &nbsp; (as it doesn't refer to the nation of Cuba).
;Also see:
:* &nbsp; Wikipedia entry: &nbsp; &nbsp; [[wp:Cuban_prime|cuban prime]].
:* &nbsp; MathWorld entry: &nbsp; [http://mathworld.wolfram.com/CubanPrime.html cuban prime].
:* &nbsp; The OEIS entry: &nbsp; &nbsp; [[oeis:A002407|A002407]]. &nbsp; &nbsp; The &nbsp; 100,000<sup>th</sup> &nbsp; cuban prime can be verified in the &nbsp; 2<sup>nd</sup> &nbsp; ''example'' &nbsp; on this OEIS web page.
<br><br>

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Task/Cuban-primes/ALGOL-68/cuban-primes.alg Normal file
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BEGIN
# find some cuban primes (using the definition: a prime p is a cuban prime if #
# p = n^3 - ( n - 1 )^3 #
# for some n > 0) #
# returns a string representation of n with commas #
PROC commatise = ( LONG INT n )STRING:
BEGIN
STRING result := "";
STRING unformatted = whole( n, 0 );
INT ch count := 0;
FOR c FROM UPB unformatted BY -1 TO LWB unformatted DO
IF ch count <= 2 THEN ch count +:= 1
ELSE ch count := 1; "," +=: result
FI;
unformatted[ c ] +=: result
OD;
result
END # commatise # ;
# sieve the primes #
INT sieve max = 2 000 000;
[ sieve max ]BOOL sieve; FOR i TO UPB sieve DO sieve[ i ] := TRUE OD;
sieve[ 1 ] := FALSE;
FOR s FROM 2 TO ENTIER sqrt( sieve max ) DO
IF sieve[ s ] THEN
FOR p FROM s * s BY s TO sieve max DO sieve[ p ] := FALSE OD
FI
OD;
# count the primes, we can ignore 2, as we know it isn't a cuban prime #
sieve[ 2 ] := FALSE;
INT prime count := 0;
FOR s TO UPB sieve DO IF sieve[ s ] THEN prime count +:= 1 FI OD;
# construct a list of the primes #
[ 1 : prime count ]INT primes;
INT prime pos := LWB primes;
FOR s FROM LWB sieve TO UPB sieve DO
IF sieve[ s ] THEN primes[ prime pos ] := s; prime pos +:= 1 FI
OD;
# find the cuban primes #
INT cuban count := 0;
LONG INT final cuban := 0;
INT max cuban = 100 000; # mximum number of cubans to find #
INT print limit = 200; # show all cubans up to this one #
print( ( "First ", commatise( print limit ), " cuban primes: ", newline ) );
LONG INT prev cube := 1;
FOR n FROM 2 WHILE
LONG INT this cube = ( LENG n * n ) * n;
LONG INT p = this cube - prev cube;
prev cube := this cube;
IF ODD p THEN
# 2 is not a cuban prime so we only test odd numbers #
BOOL is prime := TRUE;
INT max factor = SHORTEN ENTIER long sqrt( p );
FOR f FROM LWB primes WHILE is prime AND primes[ f ] <= max factor DO
is prime := p MOD primes[ f ] /= 0
OD;
IF is prime THEN
# have a cuban prime #
cuban count +:= 1;
IF cuban count <= print limit THEN
# must show this cuban #
STRING p formatted = commatise( p );
print( ( " "[ UPB p formatted : ], p formatted ) );
IF cuban count MOD 10 = 0 THEN print( ( newline ) ) FI
FI;
final cuban := p
FI
FI;
cuban count < max cuban
DO SKIP OD;
IF cuban count MOD 10 /= 0 THEN print( ( newline ) ) FI;
print( ( "The ", commatise( max cuban ), " cuban prime is: ", commatise( final cuban ), newline ) )
END

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Task/Cuban-primes/AppleScript/cuban-primes-1.applescript Normal file
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on isPrime(n)
-- Most of the numbers tested in this script will be huge
-- and none will be less than 7 or divisible by 2, 3, or 5.
(* if (n < 7) then return (n is in {2, 3, 5})
if ((n mod 2) * (n mod 3) * (n mod 5) = 0) then return false *)
repeat with i from 7 to (n ^ 0.5 div 1) by 30
if ((n mod i) * (n mod (i + 4)) * (n mod (i + 6)) * (n mod (i + 10)) * ¬
(n mod (i + 12)) * (n mod (i + 16)) * (n mod (i + 22)) * (n mod (i + 24)) = 0) then ¬
return false
end repeat
return true
end isPrime
on join(lst, delim)
set astid to AppleScript's text item delimiters
set AppleScript's text item delimiters to delim
set txt to lst as text
set AppleScript's text item delimiters to astid
return txt
end join
on intToText(int, separator)
set groups to {}
repeat while (int > 999)
set groups's beginning to ((1000 + (int mod 1000 as integer)) as text)'s text 2 thru 4
set int to int div 1000
end repeat
set groups's beginning to int
return join(groups, separator)
end intToText
on task()
set output to {"The first 200 cuban primes are:"}
set inc to 0
set candidate to 1
set counter to 0
set row to {}
repeat until (counter = 200)
set inc to inc + 6
set candidate to candidate + inc
if (isPrime(candidate)) then
set counter to counter + 1
set end of row to (" " & intToText(candidate, ","))'s text -11 thru -1
if ((counter) mod 8 = 0) then
set end of output to join(row, "")
set row to {}
end if
end if
end repeat
repeat until (counter = 100000)
set inc to inc + 6
set candidate to candidate + inc
if (isPrime(candidate)) then set counter to counter + 1
end repeat
set end of output to linefeed & "The 100,000th is " & intToText(candidate, ",")
return join(output, linefeed)
end task
task()

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Task/Cuban-primes/AppleScript/cuban-primes-2.applescript Normal file
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"The first 200 cuban primes are:
7 19 37 61 127 271 331 397
547 631 919 1,657 1,801 1,951 2,269 2,437
2,791 3,169 3,571 4,219 4,447 5,167 5,419 6,211
7,057 7,351 8,269 9,241 10,267 11,719 12,097 13,267
13,669 16,651 19,441 19,927 22,447 23,497 24,571 25,117
26,227 27,361 33,391 35,317 42,841 45,757 47,251 49,537
50,311 55,897 59,221 60,919 65,269 70,687 73,477 74,419
75,367 81,181 82,171 87,211 88,237 89,269 92,401 96,661
102,121 103,231 104,347 110,017 112,327 114,661 115,837 126,691
129,169 131,671 135,469 140,617 144,541 145,861 151,201 155,269
163,567 169,219 170,647 176,419 180,811 189,757 200,467 202,021
213,067 231,019 234,361 241,117 246,247 251,431 260,191 263,737
267,307 276,337 279,991 283,669 285,517 292,969 296,731 298,621
310,087 329,677 333,667 337,681 347,821 351,919 360,187 368,551
372,769 374,887 377,011 383,419 387,721 398,581 407,377 423,001
436,627 452,797 459,817 476,407 478,801 493,291 522,919 527,941
553,411 574,219 584,767 590,077 592,741 595,411 603,457 608,851
611,557 619,711 627,919 650,071 658,477 666,937 689,761 692,641
698,419 707,131 733,591 742,519 760,537 769,627 772,669 784,897
791,047 812,761 825,301 837,937 847,477 863,497 879,667 886,177
895,987 909,151 915,769 925,741 929,077 932,419 939,121 952,597
972,991 976,411 986,707 990,151 997,057 1,021,417 1,024,921 1,035,469
1,074,607 1,085,407 1,110,817 1,114,471 1,125,469 1,155,061 1,177,507 1,181,269
1,215,397 1,253,887 1,281,187 1,285,111 1,324,681 1,328,671 1,372,957 1,409,731
1,422,097 1,426,231 1,442,827 1,451,161 1,480,519 1,484,737 1,527,247 1,570,357
The 100,000th is 1,792,617,147,127"

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Task/Cuban-primes/Arturo/cuban-primes.arturo Normal file
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cubes: map 1..780000 'x -> x^3
cubans: []
i: 1
while [100000 > size cubans][
num: cubes\[i] - cubes\[i-1]
if prime? num ->
'cubans ++ num
inc 'i
]
first200primes: first.n: 200 cubans
loop split.every: 10 first200primes 'x ->
print map x 's -> pad to :string s 8
print ""
print ["The 100000th Cuban prime is" last cubans]

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Task/Cuban-primes/BASIC256/cuban-primes.basic Normal file
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function isprime(v)
if v mod 2 = 0 then return v = 2
for d = 3 To Int(Sqr(v))+1 Step 2
if v mod d = 0 then return false
next d3
return True
end function
function diff_cubes(n)
return 3*n*(n+1) + 1
end function
function padto(n, s)
outstr = ""
k = length(string(n))
for i = 1 to s-k
outstr = " " + outstr
next i
return outstr + string(n)
end function
print "Los primeros 200 primos cubanos son: "
nc = 0
i = 1
while nc < 100000
di = diff_cubes(i)
if isprime(di) then
nc += 1
if nc <= 200 then
print padto(di,8);" ";
if nc mod 10 = 0 then print
end if
if nc = 100000 then
print: print
print "El 100.000º primo cubano es ", di
exit while
end if
end if
i += 1
end while

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Task/Cuban-primes/Bracmat/cuban-primes.bracmat Normal file
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( ( cubanprimes
=
. !arg:(?N.?bigN)
& :?cubans
& (0.1.1):(?cube100k.?cube1.?count)
& 0:?i
& whl
' ( 1+!i:?i
& !i+1:?j
& !j^3:?cube2
& !cube2+-1*!cube1:?diff
& ( !diff^1/2:~(!diff^?)
| ( !count:~>!N
& !diff !cubans:?cubans
|
)
& ( !count:<!bigN
| !diff:?cube100k&~
)
& 1+!count:?count
)
& !cube2:?cube1
)
& ( columnwidth
= cols
. !arg:(%@:@(?:? [?cols)) ?
& div$(-1+!cols.3)*4+1
)
& columnwidth$!cubans:?colwidth
& \n:?table
& 0:?col
& ( format
= n col cif R
. !arg:(?n.?col)
& -1:?cif
& vap
$ ( (
=
. ( mod$(1+!cif:?cif.3):0
& -2+!col:?col
& ","
| -1+!col:?col&
)
!arg
)
. rev$!n
)
: "," ?R
& rev$(str$!R):?R
& whl
' ( !col+-1:?col:>-2
& " " !R:?R
)
& str$!R
)
& whl
' ( !cubans:%?cuban ?cubans
& mod$(1+!col:?col.10):?col
& (!col:0&\n|" ")
format$(!cuban.!colwidth)
!table
: ?table
)
& out$(str$("The first " !N " cuban primes are: " !table))
& out
$ ( str
$ ( "The 100,000th cuban prime is "
format$(!cube100k.columnwidth$!cube100k)
)
)
)
& cubanprimes$(200.100000)
)

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Task/Cuban-primes/C++/cuban-primes.cpp Normal file
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#include <iostream>
#include <vector>
#include <chrono>
#include <climits>
#include <cmath>
using namespace std;
vector <long long> primes{ 3, 5 };
int main()
{
cout.imbue(locale(""));
const int cutOff = 200, bigUn = 100000,
chunks = 50, little = bigUn / chunks;
const char tn[] = " cuban prime";
cout << "The first " << cutOff << tn << "s:" << endl;
int c = 0;
bool showEach = true;
long long u = 0, v = 1;
auto st = chrono::system_clock::now();
for (long long i = 1; i <= LLONG_MAX; i++)
{
bool found = false;
long long mx = (long long)(ceil(sqrt(v += (u += 6))));
for (long long item : primes)
{
if (item > mx) break;
if (v % item == 0) { found = true; break; }
}
if (!found)
{
c += 1; if (showEach)
{
for (long long z = primes.back() + 2; z <= v - 2; z += 2)
{
bool fnd = false;
for (long long item : primes)
{
if (item > mx) break;
if (z % item == 0) { fnd = true; break; }
}
if (!fnd) primes.push_back(z);
}
primes.push_back(v); cout.width(11); cout << v;
if (c % 10 == 0) cout << endl;
if (c == cutOff)
{
showEach = false;
cout << "\nProgress to the " << bigUn << "th" << tn << ": ";
}
}
if (c % little == 0) { cout << "."; if (c == bigUn) break; }
}
}
cout << "\nThe " << c << "th" << tn << " is " << v;
chrono::duration<double> elapsed_seconds = chrono::system_clock::now() - st;
cout << "\nComputation time was " << elapsed_seconds.count() << " seconds" << endl;
return 0;
}

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Task/Cuban-primes/C-sharp/cuban-primes.cs Normal file
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using System;
using System.Collections.Generic;
using System.Linq;
static class Program
{
static List<long> primes = new List<long>() { 3, 5 };
static void Main(string[] args)
{
const int cutOff = 200;
const int bigUn = 100000;
const int chunks = 50;
const int little = bigUn / chunks;
const string tn = " cuban prime";
Console.WriteLine("The first {0:n0}{1}s:", cutOff, tn);
int c = 0;
bool showEach = true;
long u = 0, v = 1;
DateTime st = DateTime.Now;
for (long i = 1; i <= long.MaxValue; i++)
{
bool found = false;
int mx = System.Convert.ToInt32(Math.Ceiling(Math.Sqrt(v += (u += 6))));
foreach (long item in primes)
{
if (item > mx) break;
if (v % item == 0) { found = true; break; }
}
if (!found)
{
c += 1; if (showEach)
{
for (var z = primes.Last() + 2; z <= v - 2; z += 2)
{
bool fnd = false;
foreach (long item in primes)
{
if (item > mx) break;
if (z % item == 0) { fnd = true; break; }
}
if (!fnd) primes.Add(z);
}
primes.Add(v); Console.Write("{0,11:n0}", v);
if (c % 10 == 0) Console.WriteLine();
if (c == cutOff)
{
showEach = false;
Console.Write("\nProgress to the {0:n0}th{1}: ", bigUn, tn);
}
}
if (c % little == 0) { Console.Write("."); if (c == bigUn) break; }
}
}
Console.WriteLine("\nThe {1:n0}th{2} is {0,17:n0}", v, c, tn);
Console.WriteLine("Computation time was {0} seconds", (DateTime.Now - st).TotalSeconds);
if (System.Diagnostics.Debugger.IsAttached) Console.ReadKey();
}
}

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Task/Cuban-primes/C/cuban-primes-1.c Normal file
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#include <limits.h>
#include <math.h>
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
typedef long long llong_t;
struct PrimeArray {
llong_t *ptr;
size_t size;
size_t capacity;
};
struct PrimeArray allocate() {
struct PrimeArray primes;
primes.size = 0;
primes.capacity = 10;
primes.ptr = malloc(primes.capacity * sizeof(llong_t));
return primes;
}
void deallocate(struct PrimeArray *primes) {
free(primes->ptr);
primes->ptr = NULL;
}
void push_back(struct PrimeArray *primes, llong_t p) {
if (primes->size >= primes->capacity) {
size_t new_capacity = (3 * primes->capacity) / 2 + 1;
llong_t *temp = realloc(primes->ptr, new_capacity * sizeof(llong_t));
if (NULL == temp) {
fprintf(stderr, "Failed to reallocate the prime array.");
exit(1);
} else {
primes->ptr = temp;
primes->capacity = new_capacity;
}
}
primes->ptr[primes->size++] = p;
}
int main() {
const int cutOff = 200, bigUn = 100000, chunks = 50, little = bigUn / chunks;
struct PrimeArray primes = allocate();
int c = 0;
bool showEach = true;
llong_t u = 0, v = 1, i;
push_back(&primes, 3);
push_back(&primes, 5);
printf("The first %d cuban primes:\n", cutOff);
for (i = 1; i < LLONG_MAX; ++i) {
bool found = false;
llong_t mx = ceil(sqrt(v += (u += 6)));
llong_t j;
for (j = 0; j < primes.size; ++j) {
if (primes.ptr[j] > mx) {
break;
}
if (v % primes.ptr[j] == 0) {
found = true;
break;
}
}
if (!found) {
c += 1;
if (showEach) {
llong_t z;
for (z = primes.ptr[primes.size - 1] + 2; z <= v - 2; z += 2) {
bool fnd = false;
for (j = 0; j < primes.size; ++j) {
if (primes.ptr[j] > mx) {
break;
}
if (z % primes.ptr[j] == 0) {
fnd = true;
break;
}
}
if (!fnd) {
push_back(&primes, z);
}
}
push_back(&primes, v);
printf("%11lld", v);
if (c % 10 == 0) {
printf("\n");
}
if (c == cutOff) {
showEach = false;
printf("\nProgress to the %dth cuban prime: ", bigUn);
}
}
if (c % little == 0) {
printf(".");
if (c == bigUn) {
break;
}
}
}
}
printf("\nThe %dth cuban prime is %lld\n", c, v);
deallocate(&primes);
return 0;
}

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Task/Cuban-primes/C/cuban-primes-2.c Normal file
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#include <gmp.h>
#include <stdio.h>
typedef unsigned long int uint;
int main(void)
{
mpz_t a, b;
mpz_init(a);
mpz_init(b);
int found = 0;
int col = 0;
for (uint n = 1; ; n++) {
mpz_ui_pow_ui(a, n, 3);
mpz_ui_pow_ui(b, n + 1, 3);
mpz_sub(a, b, a);
if (!mpz_probab_prime_p(a, 5)) continue;
if (++found <= 200) {
gmp_printf("%10Zu", a);
if (++col == 8) {
putchar('\n');
col = 0;
}
} else if (found == 100000) {
gmp_printf("100000th: %Zu\n", a);
} else if (found == 1000000) {
gmp_printf("1000000th: %Zu\n", a);
break;
}
}
return 0;
}

37
Task/Cuban-primes/Common-Lisp/cuban-primes.lisp Normal file
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;;; Show the first 200 and the 100,000th cuban prime.
;;; Cuban primes are the difference of 2 consecutive cubes.
(defun primep (n)
(cond ((< n 4) t)
((evenp n) nil)
((zerop (mod n 3)) nil)
(t (loop for i from 5 upto (isqrt n) by 6
when (or
(zerop (mod n i))
(zerop (mod n (+ i 2))))
return nil
finally (return t)))))
(defun cube (n) (* n n n))
(defun cuban (n)
(loop for i from 1
for j from 2
for cube-diff = (- (cube j) (cube i))
when (primep cube-diff)
collect cube-diff into cuban-primes
and count i into counter
when (= counter n)
return cuban-primes))
(format t "~a~%" "1st to 200th cuban prime numbers:")
(format t
"~{~<~%~,120:;~10:d ~>~}~%"
(cuban 200))
(format t "~%100,000th cuban prime number = ~:d"
(car (last (cuban 100000))))
(princ #\newline)

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Task/Cuban-primes/D/cuban-primes.d Normal file
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import std.math;
import std.stdio;
void main() {
long[] primes = [3, 5];
immutable cutOff = 200;
immutable bigUn = 100_000;
immutable chunks = 50;
immutable little = bigUn / chunks;
immutable tn = " cuban prime";
writefln("The first %s%ss:", cutOff, tn);
int c;
bool showEach = true;
long u;
long v = 1;
for (long i = 1; i > 0; ++i) {
bool found;
u += 6;
v += u;
int mx = cast(int)ceil(sqrt(cast(real)v));
foreach (item; primes) {
if (item > mx) break;
if (v % item == 0) {
found = true;
break;
}
}
if (!found) {
c++;
if (showEach) {
for (auto z = primes[$-1] + 2; z <= v - 2; z += 2) {
bool fnd;
foreach (item; primes) {
if (item > mx) break;
if (z % item == 0) {
fnd = true;
break;
}
}
if (!fnd) {
primes ~= z;
}
}
primes ~= v;
writef("%11d", v);
if (c % 10 == 0) writeln;
if (c == cutOff) {
showEach = false;
writef("\nProgress to the %sth%s: ", bigUn, tn);
}
}
if (c % little == 0) {
write('.');
if (c == bigUn) {
break;
}
}
}
}
writefln("\nThe %sth%s is %17s", c, tn, v);
}

3
Task/Cuban-primes/F-Sharp/cuban-primes-1.fs Normal file
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// Generate cuban primes. Nigel Galloway: June 9th., 2019
let cubans=Seq.unfold(fun n->Some(n*n*n,n+1L)) 1L|>Seq.pairwise|>Seq.map(fun(n,g)->g-n)|>Seq.filter(isPrime64)
let cL=let g=System.Globalization.CultureInfo("en-GB") in (fun (n:int64)->n.ToString("N0",g))

1
Task/Cuban-primes/F-Sharp/cuban-primes-2.fs Normal file
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cubans|>Seq.take 200|>List.ofSeq|>List.iteri(fun n g->if n%8=7 then printfn "%12s" (cL(g)) else printf "%12s" (cL(g)))

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Task/Cuban-primes/F-Sharp/cuban-primes-3.fs Normal file
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printfn "\n\n%s" (cL(Seq.item 99999 cubans))

13
Task/Cuban-primes/Factor/cuban-primes.factor Normal file
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USING: formatting grouping io kernel lists lists.lazy math
math.primes sequences tools.memory.private ;
IN: rosetta-code.cuban-primes
: cuban-primes ( n -- seq )
1 lfrom [ [ 3 * ] [ 1 + * ] bi 1 + ] <lazy-map>
[ prime? ] <lazy-filter> ltake list>array ;
200 cuban-primes 10 <groups>
[ [ commas ] map [ "%10s" printf ] each nl ] each nl
1e5 cuban-primes last commas "100,000th cuban prime is: %s\n"
printf

43
Task/Cuban-primes/Forth/cuban-primes.fth Normal file
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include ./miller-rabin.fs
\ commatized print
\
: d.,r ( d n -- ) \ write double precision int, commatized.
>r tuck dabs
<# begin 2dup 1.000 d> while # # # [char] , hold repeat #s rot sign #>
r> over - spaces type ;
: .,r ( n1 n2 -- ) \ write integer commatized.
>r s>d r> d.,r ;
\ generate and print cuban primes
\
: sq s" dup *" evaluate ; immediate
: next-cuban ( n -- n' p )
begin
1+ dup sq 3 * 1+ dup 3 and 0= \ first check == 0 (mod 4)
if 2 rshift dup prime?
if exit
else drop
then
else drop
then
again ;
: task1
1
20 0 do
cr 10 0 do
next-cuban 12 .,r
loop
loop drop ;
: task2
cr ." The 100,000th cuban prime is "
1 99999 0 do next-cuban drop loop next-cuban 0 .,r drop ;
task1 cr
task2 cr
bye

37
Task/Cuban-primes/FreeBASIC/cuban-primes.basic Normal file
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function isprime( n as ulongint ) as boolean
if n mod 2 = 0 then return false
for i as uinteger = 3 to int(sqr(n))+1 step 2
if n mod i = 0 then return false
next i
return true
end function
function diff_cubes( n as uinteger ) as ulongint
return 3*n*(n+1) + 1
end function
function padto( n as uinteger, s as integer ) as string
dim as string outstr=""
dim as integer k = len(str(n))
for i as integer = 1 to s-k
outstr = " " + outstr
next i
return outstr + str(n)
end function
dim as integer nc = 0, i = 1, di
while nc < 100000
di = diff_cubes(i)
if isprime(di) then
nc += 1
if nc <= 200 then
print padto(di,8);" ";
if nc mod 10 = 0 then print
end if
if nc = 100000 then
print : print : print di
exit while
end if
end if
i += 1
wend

46
Task/Cuban-primes/Go/cuban-primes.go Normal file
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package main
import (
"fmt"
"math/big"
)
func commatize(n uint64) string {
s := fmt.Sprintf("%d", n)
le := len(s)
for i := le - 3; i >= 1; i -= 3 {
s = s[0:i] + "," + s[i:]
}
return s
}
func main() {
var z big.Int
var cube1, cube2, cube100k, diff uint64
cubans := make([]string, 200)
cube1 = 1
count := 0
for i := 1; ; i++ {
j := i + 1
cube2 = uint64(j * j * j)
diff = cube2 - cube1
z.SetUint64(diff)
if z.ProbablyPrime(0) { // 100% accurate for z < 2 ^ 64
if count < 200 {
cubans[count] = commatize(diff)
}
count++
if count == 100000 {
cube100k = diff
break
}
}
cube1 = cube2
}
fmt.Println("The first 200 cuban primes are:-")
for i := 0; i < 20; i++ {
j := i * 10
fmt.Printf("%9s\n", cubans[j : j+10]) // 10 per line say
}
fmt.Println("\nThe 100,000th cuban prime is", commatize(cube100k))
}

56
Task/Cuban-primes/Groovy/cuban-primes.groovy Normal file
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class CubanPrimes {
private static int MAX = 1_400_000
private static boolean[] primes = new boolean[MAX]
static void main(String[] args) {
preCompute()
cubanPrime(200, true)
for (int i = 1; i <= 5; i++) {
int max = (int) Math.pow(10, i)
printf("%,d-th cuban prime = %,d%n", max, cubanPrime(max, false))
}
}
private static long cubanPrime(int n, boolean display) {
int count = 0
long result = 0
for (long i = 0; count < n; i++) {
long test = 1l + 3 * i * (i + 1)
if (isPrime(test)) {
count++
result = test
if (display) {
printf("%10s%s", String.format("%,d", test), count % 10 == 0 ? "\n" : "")
}
}
}
return result
}
private static boolean isPrime(long n) {
if (n < MAX) {
return primes[(int) n]
}
int max = (int) Math.sqrt(n)
for (int i = 3; i <= max; i++) {
if (primes[i] && n % i == 0) {
return false
}
}
return true
}
private static final void preCompute() {
// 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
}
}
}
}
}

15
Task/Cuban-primes/Haskell/cuban-primes-1.hs Normal file
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import Data.Numbers.Primes (isPrime)
import Data.List (intercalate)
import Data.List.Split (chunksOf)
import Text.Printf (printf)
cubans :: [Int]
cubans = filter isPrime . map (\x -> (succ x ^ 3) - (x ^ 3)) $ [1 ..]
main :: IO ()
main = do
mapM_ (\row -> mapM_ (printf "%10s" . thousands) row >> printf "\n") $ rows cubans
printf "\nThe 100,000th cuban prime is: %10s\n" $ thousands $ cubans !! 99999
where
rows = chunksOf 10 . take 200
thousands = reverse . intercalate "," . chunksOf 3 . reverse . show

6
Task/Cuban-primes/Haskell/cuban-primes-2.hs Normal file
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cubans :: [Int]
cubans =
[ x
| n <- [1 ..]
, let x = (succ n ^ 3) - (n ^ 3)
, isPrime x ]

60
Task/Cuban-primes/J/cuban-primes.j Normal file
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isPrime =: 1&p:
assert 1 0 -: isPrime 3 9
NB. difference, but first cube, of incremented y with y
dcc =: -&(^&3)~ >:
assert ((8 9 13^3)-7 8 12^3) -: dcc 7 8 12
Filter =: (#~`)(`:6)
assert 2 3 5 7 11 13 -: isPrime Filter i. 16
cubanPrime =: [: isPrime Filter dcc
assert 7 19 37 61 127 271 331 397 547 631 919 -: cubanPrime i. 20
NB. comatose copies with comma fill
comatose =: (#!.','~ (1 1 1j1 1 1 1j1 1 1 1j1 1 1 1j1 1 1 1j1 1 1 1j1 1 1 1 {.~ -@:#))@:":&>
assert (comatose 1000 1238 12 989832) -: [;._2 ] 0 :0
1,000
1,238
12
989,832
)
CP =: cubanPrime i. 800000x
# CP NB. tally, I've stored more than 100000 cuban primes
103278
NB. granted, I used wolframalpha Solve[(n+1)^3-n^3==1792617147127,n]
9!:17]2 2 NB. specify bottom right position in box
comatose&.> 10 20 $ CP
┌─────────┬─────────┬─────────┬─────────┬─────────┬─────────┬─────────┬─────────┬─────────┬─────────┬─────────┬─────────┬─────────┬─────────┬─────────┬─────────┬─────────┬─────────┬─────────┬─────────┐
│ 7│ 19│ 37│ 61│ 127│ 271│ 331│ 397│ 547│ 631│ 919│ 1,657│ 1,801│ 1,951│ 2,269│ 2,437│ 2,791│ 3,169│ 3,571│ 4,219│
├─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┤
│ 4,447│ 5,167│ 5,419│ 6,211│ 7,057│ 7,351│ 8,269│ 9,241│ 10,267│ 11,719│ 12,097│ 13,267│ 13,669│ 16,651│ 19,441│ 19,927│ 22,447│ 23,497│ 24,571│ 25,117│
├─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┤
│ 26,227│ 27,361│ 33,391│ 35,317│ 42,841│ 45,757│ 47,251│ 49,537│ 50,311│ 55,897│ 59,221│ 60,919│ 65,269│ 70,687│ 73,477│ 74,419│ 75,367│ 81,181│ 82,171│ 87,211│
├─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┤
│ 88,237│ 89,269│ 92,401│ 96,661│ 102,121│ 103,231│ 104,347│ 110,017│ 112,327│ 114,661│ 115,837│ 126,691│ 129,169│ 131,671│ 135,469│ 140,617│ 144,541│ 145,861│ 151,201│ 155,269│
├─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┤
│ 163,567│ 169,219│ 170,647│ 176,419│ 180,811│ 189,757│ 200,467│ 202,021│ 213,067│ 231,019│ 234,361│ 241,117│ 246,247│ 251,431│ 260,191│ 263,737│ 267,307│ 276,337│ 279,991│ 283,669│
├─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┤
│ 285,517│ 292,969│ 296,731│ 298,621│ 310,087│ 329,677│ 333,667│ 337,681│ 347,821│ 351,919│ 360,187│ 368,551│ 372,769│ 374,887│ 377,011│ 383,419│ 387,721│ 398,581│ 407,377│ 423,001│
├─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┤
│ 436,627│ 452,797│ 459,817│ 476,407│ 478,801│ 493,291│ 522,919│ 527,941│ 553,411│ 574,219│ 584,767│ 590,077│ 592,741│ 595,411│ 603,457│ 608,851│ 611,557│ 619,711│ 627,919│ 650,071│
├─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┤
│ 658,477│ 666,937│ 689,761│ 692,641│ 698,419│ 707,131│ 733,591│ 742,519│ 760,537│ 769,627│ 772,669│ 784,897│ 791,047│ 812,761│ 825,301│ 837,937│ 847,477│ 863,497│ 879,667│ 886,177│
├─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┤
│ 895,987│ 909,151│ 915,769│ 925,741│ 929,077│ 932,419│ 939,121│ 952,597│ 972,991│ 976,411│ 986,707│ 990,151│ 997,057│1,021,417│1,024,921│1,035,469│1,074,607│1,085,407│1,110,817│1,114,471│
├─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┤
│1,125,469│1,155,061│1,177,507│1,181,269│1,215,397│1,253,887│1,281,187│1,285,111│1,324,681│1,328,671│1,372,957│1,409,731│1,422,097│1,426,231│1,442,827│1,451,161│1,480,519│1,484,737│1,527,247│1,570,357│
└─────────┴─────────┴─────────┴─────────┴─────────┴─────────┴─────────┴─────────┴─────────┴─────────┴─────────┴─────────┴─────────┴─────────┴─────────┴─────────┴─────────┴─────────┴─────────┴─────────┘
NB. the one hundred thousandth cuban prime
comatose (<: 100000) { CP
1,792,617,147,127
cubanPrime f. NB. cubanPrime with fixed adverbs
[: (#~ 1&p:) (-&(^&3)~ >:)

57
Task/Cuban-primes/Java/cuban-primes.java Normal file
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public class CubanPrimes {
private static int MAX = 1_400_000;
private static boolean[] primes = new boolean[MAX];
public static void main(String[] args) {
preCompute();
cubanPrime(200, true);
for ( int i = 1 ; i <= 5 ; i++ ) {
int max = (int) Math.pow(10, i);
System.out.printf("%,d-th cuban prime = %,d%n", max, cubanPrime(max, false));
}
}
private static long cubanPrime(int n, boolean display) {
int count = 0;
long result = 0;
for ( long i = 0 ; count < n ; i++ ) {
long test = 1l + 3 * i * (i+1);
if ( isPrime(test) ) {
count++;
result = test;
if ( display ) {
System.out.printf("%10s%s", String.format("%,d", test), count % 10 == 0 ? "\n" : "");
}
}
}
return result;
}
private static boolean isPrime(long n) {
if ( n < MAX ) {
return primes[(int)n];
}
int max = (int) Math.sqrt(n);
for ( int i = 3 ; i <= max ; i++ ) {
if ( primes[i] && n % i == 0 ) {
return false;
}
}
return true;
}
private static final void preCompute() {
// 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;
}
}
}
}
}

14
Task/Cuban-primes/Jq/cuban-primes-1.jq Normal file
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# input should be a non-negative integer
def commatize:
def digits: tostring | explode | reverse;
[foreach digits[] as $d (-1; .+1;
(select(. > 0 and . % 3 == 0)|44), $d)] # "," is 44
| reverse | implode ;
def count(stream): reduce stream as $i (0; .+1);
def lpad($len): tostring | ($len - length) as $l | (" " * $l)[:$l] + .;
def nwise($n):
def n: if length <= $n then . else .[0:$n] , (.[$n:] | n) end;
n;

13
Task/Cuban-primes/Jq/cuban-primes-2.jq Normal file
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# Emit an unbounded stream
# The differences between successive cubes: 3n(n+1)+1
def cubanprimes:
foreach range(1;infinite) as $i (null;
(3 * $i * ($i + 1) + 1) as $d
| if $d|is_prime then $d else null end;
select(.) );
(200
| "The first \(.) cuban primes are:",
([limit(.; cubanprimes) | commatize | lpad(10)] | nwise(10) | join(" "))),
"\nThe 100,000th cuban prime is \(nth(100000 - 1; cubanprimes) | commatize)"

25
Task/Cuban-primes/Julia/cuban-primes.julia Normal file
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using Primes
function cubanprimes(N)
cubans = zeros(Int, N)
cube100k, cube1, count = 0, 1, 1
for i in Iterators.countfrom(1)
j = BigInt(i + 1)
cube2 = j^3
diff = cube2 - cube1
if isprime(diff)
count ≤ N && (cubans[count] = diff)
if count == 100000
cube100k = diff
break
end
count += 1
end
cube1 = cube2
end
println("The first $N cuban primes are: ")
foreach(x -> print(lpad(cubans[x] == 0 ? "" : cubans[x], 10), x % 8 == 0 ? "\n" : ""), 1:N)
println("\nThe 100,000th cuban prime is ", cube100k)
end
cubanprimes(200)

63
Task/Cuban-primes/Kotlin/cuban-primes.kotlin Normal file
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import kotlin.math.ceil
import kotlin.math.sqrt
fun main() {
val primes = mutableListOf(3L, 5L)
val cutOff = 200
val bigUn = 100_000
val chunks = 50
val little = bigUn / chunks
println("The first $cutOff cuban primes:")
var showEach = true
var c = 0
var u = 0L
var v = 1L
var i = 1L
while (i > 0) {
var found = false
u += 6
v += u
val mx = ceil(sqrt(v.toDouble())).toInt()
for (item in primes) {
if (item > mx) break
if (v % item == 0L) {
found = true
break
}
}
if (!found) {
c++
if (showEach) {
var z = primes.last() + 2
while (z <= v - 2) {
var fnd = false
for (item in primes) {
if (item > mx) break
if (z % item == 0L) {
fnd = true
break
}
}
if (!fnd) {
primes.add(z)
}
z += 2
}
primes.add(v)
print("%11d".format(v))
if (c % 10 == 0) println()
if (c == cutOff) {
showEach = false
print("\nProgress to the ${bigUn}th cuban prime: ")
}
}
if (c % little == 0) {
print(".")
if (c == bigUn) break
}
}
i++
}
println("\nThe %dth cuban prime is %17d".format(c, v))
}

70
Task/Cuban-primes/Lua/cuban-primes-1.lua Normal file
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local primes = {3, 5}
local cutOff = 200
local bigUn = 100000
local chunks = 50
local little = math.floor(bigUn / chunks)
local tn = " cuban prime"
print(string.format("The first %d%ss", cutOff, tn))
local showEach = true
local c = 0
local u = 0
local v = 1
for i=1,10000000000000 do
local found = false
u = u + 6
v = v + u
local mx = math.ceil(math.sqrt(v))
--for _,item in pairs(primes) do -- why: latent traversal bugfix (and performance), 6/11/2020 db
for _,item in ipairs(primes) do
if item > mx then
break
end
if v % item == 0 then
--print("[DEBUG] :( i = " .. i .. "; v = " .. v)
found = true
break
end
end
if not found then
--print("[DEBUG] :) i = " .. i .. "; v = " .. v)
c = c + 1
if showEach then
--local z = primes[table.getn(primes)] + 2 -- why: modernize (deprecated), 6/11/2020 db
local z = primes[#primes] + 2
while z <= v - 2 do
local fnd = false
--for _,item in pairs(primes) do -- why: latent traversal bugfix (and performance), 6/11/2020 db
for _,item in ipairs(primes) do
if item > mx then
break
end
if z % item == 0 then
fnd = true
break
end
end
if not fnd then
table.insert(primes, z)
end
z = z + 2
end
table.insert(primes, v)
io.write(string.format("%11d", v))
if c % 10 == 0 then
print()
end
if c == cutOff then
showEach = false
io.write(string.format("\nProgress to the %dth%s: ", bigUn, tn))
end
end
if c % little == 0 then
io.write(".")
if c == bigUn then
break
end
end
end
end
--print(string.format("\nThe %dth%s is %17d", c, tn, v)) -- why: correcting reported inaccuracy in output, 6/11/2020 db
print(string.format("\nThe %dth%s is %.0f", c, tn, v))

42
Task/Cuban-primes/Lua/cuban-primes-2.lua Normal file
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-- cuban primes in Lua (alternate version 6/12/2020 db)
------------------
-- PRIME SUPPORT:
------------------
local sqrt, sieve, primes, N = math.sqrt, {false}, {}, 1400000
for i = 2,N do sieve[i]=true end
for i = 2,N do if sieve[i] then for j=i*i,N,i do sieve[j]=false end end end
for i = 2,N do if sieve[i] then primes[#primes+1]=i end end; sieve=nil
local function isprime(n)
if (n <= 1) then return false end
local limit = sqrt(n)
for i,p in ipairs(primes) do
if (n % p == 0) then return false end
if (p > limit) then return true end
end
error("insufficient list of primes")
end
------------------
-- PRINT SUPPORT:
------------------
local write, format = io.write, string.format
local function commafy(i) return tostring(i):reverse():gsub("(%d%d%d)","%1,"):reverse():gsub("^,","") end
----------------
-- ACTUAL TASK:
----------------
local COUNT, DOTAT, DOTPER, count, n = 100000, 200, 2000, 0, 0
while (count < COUNT) do
local h = 3 * n * (n + 1) + 1 -- A003215
if (isprime(h)) then
count = count + 1
if (count <= DOTAT) then
write(format("%11s%s", commafy(h), count%10==0 and "\n" or ""))
elseif (count == COUNT) then
print(format("\n%s", commafy(h)))
elseif (count % DOTPER == 0) then
write(".")
end
end
n = n + 1
end

9
Task/Cuban-primes/Maple/cuban-primes.maple Normal file
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CubanPrimes := proc(n) local i, cp;
cp := Array([]);
for i by 2 while numelems(cp) < n do
if isprime(3/4*i^2 + 1/4) then
ArrayTools:-Append(cp, 3/4*i^2 + 1/4);
end if;
end do;
return cp;
end proc;

8
Task/Cuban-primes/Mathematica/cuban-primes.math Normal file
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cubans[m_Integer] := Block[{n = 1, result = {}, candidate},
While[Length[result] < m,
n++;
candidate = n^3 - (n - 1)^3;
If[PrimeQ[candidate], AppendTo[result, candidate]]];
result]
cubans[200]
NumberForm[Last[cubans[100000]], NumberSeparator -> ",", DigitBlock -> 3]

53
Task/Cuban-primes/Nim/cuban-primes.nim Normal file
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import strformat
import strutils
import math
const cutOff = 200
const bigUn = 100000
const chunks = 50
const little = bigUn div chunks
echo fmt"The first {cutOff} cuban primes"
var primes: seq[int] = @[3, 5]
var c, u = 0
var showEach: bool = true
var v = 1
for i in 1..high(BiggestInt):
var found: bool
inc u, 6
inc v, u
var mx = int(ceil(sqrt(float(v))))
for item in primes:
if item > mx:
break
if v mod item == 0:
found = true
break
if not found:
inc c
if showEach:
for z in countup(primes[^1] + 2, v - 2, step=2):
var fnd: bool = false
for item in primes:
if item > mx:
break
if z mod item == 0:
fnd = true
break
if not fnd:
primes.add(z)
primes.add(v)
write(stdout, fmt"{insertSep($v, ','):>11}")
if c mod 10 == 0:
write(stdout, "\n")
if c == cutOff:
showEach = false
write(stdout, fmt"Progress to the {bigUn}th cuban prime: ")
stdout.flushFile
if c mod little == 0:
write(stdout, ".")
stdout.flushFile
if c == bigUn:
break
write(stdout, "\n")
echo fmt"The {c}th cuban prime is {insertSep($v, ',')}"

103
Task/Cuban-primes/Pascal/cuban-primes.pas Normal file
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program CubanPrimes;
{$IFDEF FPC}
{$MODE DELPHI}
{$OPTIMIZATION ON,Regvar,PEEPHOLE,CSE,ASMCSE}
{$CODEALIGN proc=32}
{$ENDIF}
uses
primTrial;
const
COLUMNCOUNT = 10*10;
procedure FormOut(Cuban:Uint64;ColSize:Uint32);
var
s : String;
pI,pJ :pChar;
i,j : NativeInt;
Begin
str(Cuban,s);
i := length(s);
If i>3 then
Begin
//extend s by the count of comma to be inserted
j := i+ (i-1) div 3;
setlength(s,j);
pI := @s[i];
pJ := @s[j];
while i > 3 do
Begin
// copy 3 digits
pJ^ := pI^;dec(pJ);dec(pI);
pJ^ := pI^;dec(pJ);dec(pI);
pJ^ := pI^;dec(pJ);dec(pI);
// insert comma
pJ^ := ',';dec(pJ);
dec(i,3);
end;
//the digits in front are in the right place
end;
write(s:ColSize);
end;
procedure OutFirstCntCubPrimes(Cnt : Int32;ColCnt : Int32);
var
cbDelta1,
cbDelta2 : Uint64;
ClCnt,ColSize : NativeInt;
Begin
If Cnt <= 0 then
EXIT;
IF ColCnt <= 0 then
ColCnt := 1;
ColSize := COLUMNCOUNT DIV ColCnt;
dec(ColCnt);
ClCnt := ColCnt;
cbDelta1 := 0;
cbDelta2 := 1;
repeat
if isPrime(cbDelta2) then
Begin
FormOut(cbDelta2,ColSize);
dec(Cnt);
dec(ClCnt);
If ClCnt < 0 then
Begin
Writeln;
ClCnt := ColCnt;
end;
end;
inc(cbDelta1,6);// 0,6,12,18...
inc(cbDelta2,cbDelta1);//1,7,19,35...
until Cnt<= 0;
writeln;
end;
procedure OutNthCubPrime(n : Int32);
var
cbDelta1,
cbDelta2 : Uint64;
Begin
If n <= 0 then
EXIT;
cbDelta1 := 0;
cbDelta2 := 1;
repeat
inc(cbDelta1,6);
inc(cbDelta2,cbDelta1);
if isPrime(cbDelta2) then
dec(n);
until n<=0;
FormOut(cbDelta2,20);
writeln;
end;
Begin
OutFirstCntCubPrimes(200,10);
OutNthCubPrime(100000);
end.

32
Task/Cuban-primes/Perl/cuban-primes.pl Normal file
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use feature 'say';
use ntheory 'is_prime';
sub cuban_primes {
my ($n) = @_;
my @primes;
for (my $k = 1 ; ; ++$k) {
my $p = 3 * $k * ($k + 1) + 1;
if (is_prime($p)) {
push @primes, $p;
last if @primes >= $n;
}
}
return @primes;
}
sub commify {
scalar reverse join ',', unpack '(A3)*', reverse shift;
}
my @c = cuban_primes(200);
while (@c) {
say join ' ', map { sprintf "%9s", commify $_ } splice(@c, 0, 10);
}
say '';
for my $n (1 .. 6) {
say "10^$n-th cuban prime is: ", commify((cuban_primes(10**$n))[-1]);
}

34
Task/Cuban-primes/Phix/cuban-primes.phix Normal file
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(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">np</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">i</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span>
<span style="color: #004080;">mpz</span> <span style="color: #000000;">p3</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">*</span><span style="color: #000000;">1</span><span style="color: #0000FF;">*</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">i3</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(),</span>
<span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(),</span>
<span style="color: #000000;">pn</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">()</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: #008000;">"The first 200 cuban primes are:\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">first200</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">lim</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()=</span><span style="color: #004600;">JS</span><span style="color: #0000FF;">?</span><span style="color: #000000;">10000</span><span style="color: #0000FF;">:</span><span style="color: #000000;">100000</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">np</span><span style="color: #0000FF;"><</span><span style="color: #000000;">lim</span> <span style="color: #008080;">do</span>
<span style="color: #7060A8;">mpz_ui_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i3</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: #7060A8;">mpz_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p3</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">mpz_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">mpz_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">np</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">np</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">200</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">first200</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">first200</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%,9d"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">mpz_get_integer</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pn</span><span style="color: #0000FF;">)))</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">mod</span><span style="color: #0000FF;">(</span><span style="color: #000000;">np</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</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: #008000;">"%s\n"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">first200</span><span style="color: #0000FF;">[-</span><span style="color: #000000;">10</span><span style="color: #0000FF;">..-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]))</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;">if</span>
<span style="color: #7060A8;">mpz_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i3</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">i</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</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: #008000;">"\nThe %,dth cuban prime is %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">np</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">comma_fill</span><span style="color: #0000FF;">:=</span><span style="color: #004600;">true</span><span style="color: #0000FF;">)})</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">p3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_free</span><span style="color: #0000FF;">({</span><span style="color: #000000;">p3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">})</span>
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)</span>
<!--

67
Task/Cuban-primes/Python/cuban-primes.py Normal file
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import datetime
import math
primes = [ 3, 5 ]
cutOff = 200
bigUn = 100_000
chunks = 50
little = bigUn / chunks
tn = " cuban prime"
print ("The first {:,}{}s:".format(cutOff, tn))
c = 0
showEach = True
u = 0
v = 1
st = datetime.datetime.now()
for i in range(1, int(math.pow(2,20))):
found = False
u += 6
v += u
mx = int(math.sqrt(v))
for item in primes:
if (item > mx):
break
if (v % item == 0):
found = True
break
if (found == 0):
c += 1
if (showEach):
z = primes[-1]
while (z <= v - 2):
z += 2
fnd = False
for item in primes:
if (item > mx):
break
if (z % item == 0):
fnd = True
break
if (not fnd):
primes.append(z)
primes.append(v)
print("{:>11,}".format(v), end='')
if (c % 10 == 0):
print("");
if (c == cutOff):
showEach = False
print ("Progress to the {:,}th {}:".format(bigUn, tn), end='')
if (c % little == 0):
print('.', end='')
if (c == bigUn):
break
print("");
print ("The {:,}th{} is {:,}".format(c, tn, v))
print("Computation time was {} seconds".format((datetime.datetime.now() - st).seconds))

27
Task/Cuban-primes/REXX/cuban-primes.rexx Normal file
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/*REXX program finds and displays a number of cuban primes or the Nth cuban prime. */
numeric digits 20 /*ensure enough decimal digits for #s. */
parse arg N . /*obtain optional argument from the CL.*/
if N=='' | N=="," then N= 200 /*Not specified? Then use the default.*/
Nth= N<0; N= abs(N) /*used for finding the Nth cuban prime.*/
@.=0; @.0=1; @.2=1; @.3=1; @.4=1; @.5=1; @.6=1; @.8=1 /*ending digs that aren't cubans.*/
sw= linesize() - 1; if sw<1 then sw= 79 /*obtain width of the terminal screen. */
w=12; #= 1; $= right(7, w) /*start with first cuban prime; count.*/
do j=1 until #=>N; x= (j+1)**3 - j**3 /*compute a possible cuban prime. */
parse var x '' -1 _; if @._ then iterate /*check last digit for non─cuban prime.*/
do k=1 until km*km>x; km= k*6 + 1 /*cuban primes can't be ÷ by 6k+1 */
if x//km==0 then iterate j /*Divisible? Then not a cuban prime. */
end /*k*/
#= #+1 /*bump the number of cuban primes found*/
if Nth then do; if #==N then do; say commas(x); leave j; end /*display 1 num.*/
else iterate /*j*/ /*keep searching*/
end /* [↑] try to fit as many #s per line.*/
cx= commas(x); L= length(cx) /*insert commas──►X; obtain the length.*/
cx= right(cx, max(w, L) ); new= $ cx /*right justify CX; concat to new list*/
if length(new)>sw then do; say $; $= cx /*line is too long, display #'s so far.*/
end /* [↑] initialize the (new) next line.*/
else $= new /*start with cuban # that wouldn't fit.*/
end /*j*/
if \Nth & $\=='' then say $ /*check for residual cuban primes in $.*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
commas: parse arg _; do jc=length(_)-3 to 1 by -3; _=insert(',', _, jc); end; return _

38
Task/Cuban-primes/Racket/cuban-primes.rkt Normal file
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#lang racket
(require math/number-theory
racket/generator)
(define (make-cuban-prime-generator)
(generator ()
(let loop ((y 1) (y3 1))
(let* ((x (+ y 1))
(x3 (expt x 3))
(p (quotient (- x3 y3) (- x y))))
(when (prime? p) (yield p))
(loop x x3)))))
(define (tabulate l (line-width 80))
(let* ((w (add1 (string-length (argmax string-length (map ~a l)))))
(cols (quotient line-width w)))
(for ((n (in-range 1 (add1 (length l))))
(i l))
(display (~a i #:width w #:align 'right))
(when (zero? (modulo n cols)) (newline)))))
(define (progress-report x)
(when (zero? (modulo x 1000))
(eprintf (if (zero? (modulo x 10000)) "|" "."))
(flush-output (current-error-port))))
(let ((200-cuban-primes (for/list ((_ 200)
(p (in-producer (make-cuban-prime-generator))))
p)))
(tabulate 200-cuban-primes))
(begin0
(for/last ((x 100000)
(p (in-producer (make-cuban-prime-generator))))
(progress-report x)
p)
(newline))

10
Task/Cuban-primes/Raku/cuban-primes-1.raku Normal file
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use Lingua::EN::Numbers;
use ntheory:from<Perl5> <:all>;
my @cubans = lazy (1..Inf).map({ ($_+1)³ - .³ }).grep: *.&is_prime;
put @cubans[^200]».&comma».fmt("%9s").rotor(10).join: "\n";
put '';
put @cubans[99_999].&comma; # zero indexed

9
Task/Cuban-primes/Raku/cuban-primes-2.raku Normal file
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sub comma { $^i.flip.comb(3).join(',').flip }
for 2..10 -> \k {
next if k %% 3;
my @cubans = lazy (1..Inf).map({ (($_+k)³ - .³)/k }).grep: *.is-prime;
put "First 20 cuban primes where k = {k}:";
put @cubans[^20]».&comma».fmt("%7s").rotor(10).join: "\n";
put '';
}

5
Task/Cuban-primes/Raku/cuban-primes-3.raku Normal file
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sub comma { $^i.flip.comb(3).join(',').flip }
my \k = 2**128;
put "First 10 cuban primes where k = {k}:";
.&comma.put for (lazy (0..Inf).map({ (($_+k)³ - .³)/k }).grep: *.is-prime)[^10];

20
Task/Cuban-primes/Ring/cuban-primes.ring Normal file
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load "stdlib.ring"
sum = 0
limit = 1000
see "First 200 cuban primes:" + nl
for n = 1 to limit
pr = pow(n+1,3) - pow(n,3)
if isprime(pr)
sum = sum + 1
if sum < 201
see "" + pr + " "
else
exit
ok
ok
next
see "done..." + nl

22
Task/Cuban-primes/Ruby/cuban-primes.rb Normal file
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require "openssl"
RE = /(\d)(?=(\d\d\d)+(?!\d))/ # Activesupport uses this for commatizing
cuban_primes = Enumerator.new do |y|
(1..).each do |n|
cand = 3*n*(n+1) + 1
y << cand if OpenSSL::BN.new(cand).prime?
end
end
def commatize(num)
num.to_s.gsub(RE, "\\1,")
end
cbs = cuban_primes.take(200)
formatted = cbs.map{|cb| commatize(cb).rjust(10) }
puts formatted.each_slice(10).map(&:join)
t0 = Time.now
puts "
100_000th cuban prime is #{commatize( cuban_primes.take(100_000).last)}
which took #{(Time.now-t0).round} seconds to calculate."

42
Task/Cuban-primes/Rust/cuban-primes.rust Normal file
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use std::time::Instant;
use separator::Separatable;
const NUMBER_OF_CUBAN_PRIMES: usize = 200;
const COLUMNS: usize = 10;
const LAST_CUBAN_PRIME: usize = 100_000;
fn main() {
println!("Calculating the first {} cuban primes and the {}th cuban prime...", NUMBER_OF_CUBAN_PRIMES, LAST_CUBAN_PRIME);
let start = Instant::now();
let mut i: u64 = 0;
let mut j: u64 = 1;
let mut index: usize = 0;
let mut cuban_primes = Vec::new();
let mut cuban: u64 = 0;
while index < 100_000 {
cuban = {j += 1; j}.pow(3) - {i += 1; i}.pow(3);
if primal::is_prime(cuban) {
if index < NUMBER_OF_CUBAN_PRIMES {
cuban_primes.push(cuban);
}
index += 1;
}
}
let elapsed = start.elapsed();
println!("THE {} FIRST CUBAN PRIMES:", NUMBER_OF_CUBAN_PRIMES);
cuban_primes
.chunks(COLUMNS)
.map(|chunk| {
chunk.iter()
.map(|item| {
print!("{}\t", item)
})
.for_each(drop);
println!("");
})
.for_each(drop);
println!("The {}th cuban prime number is {}", LAST_CUBAN_PRIME, cuban.separated_string());
println!("Elapsed time: {:?}", elapsed);
}

40
Task/Cuban-primes/Scala/cuban-primes.scala Normal file
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import spire.math.SafeLong
import spire.implicits._
import scala.annotation.tailrec
import scala.collection.parallel.immutable.ParVector
object CubanPrimes {
def main(args: Array[String]): Unit = {
println(formatTable(cubanPrimes.take(200).toVector, 10))
println(f"The 100,000th cuban prime is: ${getNthCubanPrime(100000).toBigInt}%,d")
}
def cubanPrimes: LazyList[SafeLong] = cubans.filter(isPrime)
def cubans: LazyList[SafeLong] = LazyList.iterate(SafeLong(0))(_ + 1).map(n => (n + 1).pow(3) - n.pow(3))
def isPrime(num: SafeLong): Boolean = (num > 1) && !(SafeLong(2) #:: LazyList.iterate(SafeLong(3)){n => n + 2}).takeWhile(n => n*n <= num).exists(num%_ == 0)
def getNthCubanPrime(num: Int): SafeLong = {
@tailrec
def nHelper(rem: Int, src: LazyList[SafeLong]): SafeLong = {
val cprimes = src.take(100000).to(ParVector).filter(isPrime)
if(cprimes.size < rem) nHelper(rem - cprimes.size, src.drop(100000))
else cprimes.toVector.sortWith(_<_)(rem - 1)
}
nHelper(num, cubans)
}
def formatTable(lst: Vector[SafeLong], rlen: Int): String = {
@tailrec
def fHelper(ac: Vector[String], src: Vector[String]): String = {
if(src.nonEmpty) fHelper(ac :+ src.take(rlen).mkString, src.drop(rlen))
else ac.mkString("\n")
}
val maxLen = lst.map(n => f"${n.toBigInt}%,d".length).max
val formatted = lst.map(n => s"%,${maxLen + 2}d".format(n.toInt))
fHelper(Vector[String](), formatted)
}
}

11
Task/Cuban-primes/Sidef/cuban-primes.sidef Normal file
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func cuban_primes(n) {
1..Inf -> lazy.map {|k| 3*k*(k+1) + 1 }\
.grep{ .is_prime }\
.first(n)
}
cuban_primes(200).slices(10).each {
say .map { "%9s" % .commify }.join(' ')
}
say ("\n100,000th cuban prime is: ", cuban_primes(1e5).last.commify)

47
Task/Cuban-primes/Transd/cuban-primes.transd Normal file
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#lang transd
MainModule: {
primes: Vector<ULong>([3, 5]),
lim: 200,
bigUn: 100000,
chunks: 50,
little: 0,
c: 0,
showEach: true,
u: ULong(0),
v: ULong(1),
_start: (λ found Bool() fnd Bool() mx Int() z ULong()
(= little (/ bigUn chunks))
(for i in Range(1 (pow 2 20)) do
(= found false)
(+= u 6) (+= v u) (= mx (to-Int (sqrt v) 1))
(for item in primes do
(if (> item mx) break)
(if (not (mod v item)) (= found true)
break))
(if (not found)
(+= c 1)
(if showEach
(= z (get primes -1))
(while (< z (- v 2))
(+= z 2) (= fnd false)
(for item in primes do
(if (> item mx) break)
(if (not (mod z item)) (= fnd true)
break))
(if (not fnd) (append primes z)))
(append primes v)
(textout :width 11 :group v)
(if (not (mod c 10)) (textout :nl))
(if (== c lim) (= showEach false)
(textout "Progress to the " :group bigUn
"'th cuban prime:" ))
)
(if (not (mod c little)) (textout "."))
(if (== c bigUn) break)
)
)
(lout "The " :group c "'th cuban prime is " v )
)
}

37
Task/Cuban-primes/Visual-Basic-.NET/cuban-primes-1.vb Normal file
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Module Module1
Dim primes As List(Of Long) = {3L, 5L}.ToList()
Sub Main(args As String())
Const cutOff As Integer = 200, bigUn As Integer = 100000,
tn As String = " cuban prime"
Console.WriteLine("The first {0:n0}{1}s:", cutOff, tn)
Dim c As Integer = 0, showEach As Boolean = True, skip As Boolean = True,
v As Long = 0, st As DateTime = DateTime.Now
For i As Long = 1 To Long.MaxValue
v = 3 * i : v = v * i + v + 1
Dim found As Boolean = False, mx As Integer = Math.Ceiling(Math.Sqrt(v))
For Each item In primes
If item > mx Then Exit For
If v Mod item = 0 Then found = True : Exit For
Next : If Not found Then
c += 1 : If showEach Then
For z = primes.Last + 2 To v - 2 Step 2
Dim fnd As Boolean = False
For Each item In primes
If item > mx Then Exit For
If z Mod item = 0 Then fnd = True : Exit For
Next : If Not fnd Then primes.Add(z)
Next : primes.Add(v) : Console.Write("{0,11:n0}", v)
If c Mod 10 = 0 Then Console.WriteLine()
If c = cutOff Then showEach = False
Else
If skip Then skip = False : i += 772279 : c = bigUn - 1
End If
If c = bigUn Then Exit For
End If
Next
Console.WriteLine("{1}The {2:n0}th{3} is {0,17:n0}", v, vbLf, c, tn)
Console.WriteLine("Computation time was {0} seconds", (DateTime.Now - st).TotalSeconds)
If System.Diagnostics.Debugger.IsAttached Then Console.ReadKey()
End Sub
End Module

39
Task/Cuban-primes/Visual-Basic-.NET/cuban-primes-2.vb Normal file
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Module Program
Dim primes As List(Of Long) = {3L, 5L}.ToList()
Sub Main(args As String())
Dim taskList As New List(Of Task(Of Integer))
Const cutOff As Integer = 200, bigUn As Integer = 100000,
chunks As Integer = 50, little As Integer = bigUn / chunks,
tn As String = " cuban prime"
Console.WriteLine("The first {0:n0}{1}s:", cutOff, tn)
Dim c As Integer = 0, showEach As Boolean = True,
u As Long = 0, v As Long = 1,
st As DateTime = DateTime.Now
For i As Long = 1 To Long.MaxValue
u += 6 : v += u
Dim found As Boolean = False, mx As Integer = Math.Ceiling(Math.Sqrt(v))
For Each item In primes
If item > mx Then Exit For
If v Mod item = 0 Then found = True : Exit For
Next : If Not found Then
c += 1 : If showEach Then
For z = primes.Last + 2 To v - 2 Step 2
Dim fnd As Boolean = False
For Each item In primes
If item > mx Then Exit For
If z Mod item = 0 Then fnd = True : Exit For
Next : If Not fnd Then primes.Add(z)
Next : primes.Add(v) : Console.Write("{0,11:n0}", v)
If c Mod 10 = 0 Then Console.WriteLine()
If c = cutOff Then showEach = False : _
Console.Write("{0}Progress to the {1:n0}th{2}: ", vbLf, bigUn, tn)
End If
If c Mod little = 0 Then Console.Write(".") : If c = bigUn Then Exit For
End If
Next
Console.WriteLine("{1}The {2:n0}th{3} is {0,17:n0}", v, vbLf, c, tn)
Console.WriteLine("Computation time was {0} seconds", (DateTime.Now - st).TotalSeconds)
If System.Diagnostics.Debugger.IsAttached Then Console.ReadKey()
End Sub
End Module

63
Task/Cuban-primes/Wren/cuban-primes.wren Normal file
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import "/fmt" for Fmt
var start = System.clock
var primes = [3, 5]
var cutOff = 200
var bigOne = 100000
var cubans = []
var bigCuban = ""
var c = 0
var showEach = true
var u = 0
var v = 1
for (i in 1...(1<<20)) {
var found = false
u = u + 6
v = v + u
var mx = v.sqrt.floor
for (item in primes) {
if (item > mx) break
if (v%item == 0) {
found = true
break
}
}
if (!found) {
c = c + 1
if (showEach) {
var z = primes[-1]
while (z <= v -2) {
z = z + 2
var fnd = false
for (item in primes) {
if (item > mx) break
if (z%item == 0) {
fnd = true
break
}
}
if (!fnd) {
primes.add(z)
}
}
primes.add(v)
cubans.add(Fmt.commatize(v))
if (c == cutOff) showEach = false
}
if (c == bigOne) {
bigCuban = Fmt.commatize(v)
break
}
}
}
System.print("The first 200 cuban primes are:-")
for (i in 0...20) {
var j = i * 10
for (k in j...j+10) System.write(Fmt.s(10, cubans[k])) // 10 per line say
System.print()
}
System.print("\nThe 100,000th cuban prime is %(bigCuban)")
System.print("\nTook %(System.clock - start) secs")

10
Task/Cuban-primes/Zkl/cuban-primes-1.zkl Normal file
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var [const] BI=Import("zklBigNum"); // libGMP
cubans:=(1).walker(*).tweak('wrap(n){ // lazy iterator
p:=3*n*(n + 1) + 1;
BI(p).probablyPrime() and p or Void.Skip
});
println("First 200 cuban primes:");
do(20){ (10).pump(String, cubans.next, "%10,d".fmt).println() }
cubans.drop(100_000 - cubans.n).value :
println("\nThe 100,000th cuban prime is: %,d".fmt(_));

7
Task/Cuban-primes/Zkl/cuban-primes-2.zkl Normal file
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k,z := BI(2).pow(128), 10;
println("First %d cuban primes where k = %,d:".fmt(z,k));
foreach n in ([BI(1)..]){
p:=( (k + n).pow(3) - n.pow(3) )/k;
if(p.probablyPrime()){ println("%,d".fmt(p)); z-=1; }
if(z<=0) break;
}