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Ingy döt Net 2023-07-01 11:58:00 -04:00
parent 7387c8f97b
commit cb5bb5e222
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2
Task/Descending-primes/00-META.yaml Normal file
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---
from: http://rosettacode.org/wiki/Descending_primes

9
Task/Descending-primes/00-TASK.txt Normal file
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Generate and show all primes with strictly descending decimal digits.
;See also
;* [[oeis:A052014|OEIS:A052014 - Primes with distinct digits in descending order]]
;Related:
*[[Ascending primes]]

32
Task/Descending-primes/11l/descending-primes-1.11l Normal file
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F is_prime(p)
I p < 2 | p % 2 == 0
R p == 2
L(i) (3 .. Int(sqrt(p))).step(2)
I p % i == 0
R 0B
R 1B
V c = 0
V ps = [1, 2, 3, 4, 5, 6, 7, 8, 9]
V nxt = [0] * 128
L
V nc = 0
L(a) ps
I is_prime(a)
c++
print(‘#8’.format(a), end' I c % 5 == 0 {"\n"} E ‘ ’)
V b = a * 10
V l = a % 10 + b
b++
L b < l
nxt[nc] = b
nc++
b++
I nc > 1
ps = nxt[0 .< nc]
E
L.break
print("\n"c‘ descending primes found’)

22
Task/Descending-primes/11l/descending-primes-2.11l Normal file
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F is_prime(p)
I p < 2 | p % 2 == 0
R p == 2
L(i) (3 .. Int(sqrt(p))).step(2)
I p % i == 0
R 0B
R 1B
[Int] descending_primes
L(n) 1 .< 2 ^ 9
V s = ‘’
L(i) (8 .. 0).step(-1)
I n [&] (1 << i) != 0
s ‘’= String(i + 1)
I is_prime(Int(s))
descending_primes.append(Int(s))
L(n) sorted(descending_primes)
print(‘#8’.format(n), end' I (L.index + 1) % 5 == 0 {"\n"} E ‘ ’)
print("\n"descending_primes.len‘ descending primes found’)

45
Task/Descending-primes/ALGOL-68/descending-primes.alg Normal file
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BEGIN # find all primes with strictly decreasing digits #
PR read "primes.incl.a68" PR # include prime utilities #
PR read "rows.incl.a68" PR # include array utilities #
[ 1 : 512 ]INT primes; # there will be at most 512 (2^9) primes #
INT p count := 0; # number of primes found so far #
FOR d1 FROM 0 TO 1 DO
INT n1 = IF d1 = 1 THEN 9 ELSE 0 FI;
FOR d2 FROM 0 TO 1 DO
INT n2 = IF d2 = 1 THEN ( n1 * 10 ) + 8 ELSE n1 FI;
FOR d3 FROM 0 TO 1 DO
INT n3 = IF d3 = 1 THEN ( n2 * 10 ) + 7 ELSE n2 FI;
FOR d4 FROM 0 TO 1 DO
INT n4 = IF d4 = 1 THEN ( n3 * 10 ) + 6 ELSE n3 FI;
FOR d5 FROM 0 TO 1 DO
INT n5 = IF d5 = 1 THEN ( n4 * 10 ) + 5 ELSE n4 FI;
FOR d6 FROM 0 TO 1 DO
INT n6 = IF d6 = 1 THEN ( n5 * 10 ) + 4 ELSE n5 FI;
FOR d7 FROM 0 TO 1 DO
INT n7 = IF d7 = 1 THEN ( n6 * 10 ) + 3 ELSE n6 FI;
FOR d8 FROM 0 TO 1 DO
INT n8 = IF d8 = 1 THEN ( n7 * 10 ) + 2 ELSE n7 FI;
FOR d9 FROM 0 TO 1 DO
INT n9 = IF d9 = 1 THEN ( n8 * 10 ) + 1 ELSE n8 FI;
IF n9 > 0 THEN
IF is probably prime( n9 ) THEN
# have a prime with strictly descending digits #
primes[ p count +:= 1 ] := n9
FI
FI
OD
OD
OD
OD
OD
OD
OD
OD
OD;
QUICKSORT primes FROMELEMENT 1 TOELEMENT p count; # sort the primes #
# display the primes #
FOR i TO p count DO
print( ( " ", whole( primes[ i ], -8 ) ) );
IF i MOD 10 = 0 THEN print( ( newline ) ) FI
OD
END

35
Task/Descending-primes/AWK/descending-primes.awk Normal file
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# syntax: GAWK -f DESCENDING_PRIMES.AWK
BEGIN {
start = 1
stop = 99999999
for (i=start; i<=stop; i++) {
leng = length(i)
flag = 1
for (j=1; j<leng; j++) {
if (substr(i,j,1) <= substr(i,j+1,1)) {
flag = 0
break
}
}
if (flag) {
if (is_prime(i)) {
printf("%9d%1s",i,++count%10?"":"\n")
}
}
}
printf("\n%d-%d: %d descending primes\n",start,stop,count)
exit(0)
}
function is_prime(n, d) {
d = 5
if (n < 2) { return(0) }
if (n % 2 == 0) { return(n == 2) }
if (n % 3 == 0) { return(n == 3) }
while (d*d <= n) {
if (n % d == 0) { return(0) }
d += 2
if (n % d == 0) { return(0) }
d += 4
}
return(1)
}

27
Task/Descending-primes/Arturo/descending-primes.arturo Normal file
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descending: @[
loop 1..9 'a [
loop 1..dec a 'b [
loop 1..dec b 'c [
loop 1..dec c 'd [
loop 1..dec d 'e [
loop 1..dec e 'f [
loop 1..dec f 'g [
loop 1..dec g 'h [
loop 1..dec h 'i -> @[a b c d e f g h i]
@[a b c d e f g h]]
@[a b c d e f g]]
@[a b c d e f]]
@[a b c d e]]
@[a b c d]]
@[a b c]]
@[a b]]
@[a]]
]
descending: filter descending 'd -> some? d 'n [not? positive? n]
descending: filter descending 'd -> d <> unique d
descending: sort map descending 'd -> to :integer join to [:string] d
loop split.every:10 select descending => prime? 'row [
print map to [:string] row 'item -> pad item 8
]

23
Task/Descending-primes/C++/descending-primes.cpp Normal file
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#include <iostream>
bool ispr(unsigned int n) {
if ((n & 1) == 0 || n < 2) return n == 2;
for (unsigned int j = 3; j * j <= n; j += 2)
if (n % j == 0) return false; return true; }
int main() {
unsigned int c = 0, nc, pc = 9, i, a, b, l,
ps[128]{ 1, 2, 3, 4, 5, 6, 7, 8, 9 }, nxt[128];
while (true) {
nc = 0;
for (i = 0; i < pc; i++) {
if (ispr(a = ps[i]))
printf("%8d%s", a, ++c % 5 == 0 ? "\n" : " ");
for (b = a * 10, l = a % 10 + b++; b < l; b++)
nxt[nc++] = b;
}
if (nc > 1) for(i = 0, pc = nc; i < pc; i++) ps[i] = nxt[i];
else break;
}
printf("\n%d descending primes found", c);
}

28
Task/Descending-primes/C-sharp/descending-primes.cs Normal file
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using System;
class Program {
static bool ispr(uint n) {
if ((n & 1) == 0 || n < 2) return n == 2;
for (uint j = 3; j * j <= n; j += 2)
if (n % j == 0) return false; return true; }
static void Main(string[] args) {
uint c = 0; int nc;
var ps = new uint[]{ 1, 2, 3, 4, 5, 6, 7, 8, 9 };
var nxt = new uint[128];
while (true) {
nc = 0;
foreach (var a in ps) {
if (ispr(a))
Console.Write("{0,8}{1}", a, ++c % 5 == 0 ? "\n" : " ");
for (uint b = a * 10, l = a % 10 + b++; b < l; b++)
nxt[nc++] = b;
}
if (nc > 1) {
Array.Resize (ref ps, nc); Array.Copy(nxt, ps, nc); }
else break;
}
Console.WriteLine("\n{0} descending primes found", c);
}
}

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Task/Descending-primes/C/descending-primes.c Normal file
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#include <stdio.h>
int ispr(unsigned int n) {
if ((n & 1) == 0 || n < 2) return n == 2;
for (unsigned int j = 3; j * j <= n; j += 2)
if (n % j == 0) return 0; return 1; }
int main() {
unsigned int c = 0, nc, pc = 9, i, a, b, l,
ps[128], nxt[128];
for (a = 0, b = 1; a < pc; a = b++) ps[a] = b;
while (1) {
nc = 0;
for (i = 0; i < pc; i++) {
if (ispr(a = ps[i]))
printf("%8d%s", a, ++c % 5 == 0 ? "\n" : " ");
for (b = a * 10, l = a % 10 + b++; b < l; b++)
nxt[nc++] = b;
}
if (nc > 1) for(i = 0, pc = nc; i < pc; i++) ps[i] = nxt[i];
else break;
}
printf("\n%d descending primes found", c);
}

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Task/Descending-primes/Delphi/descending-primes.delphi Normal file
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type TProgress = procedure(Percent: integer);
function IsPrime(N: integer): boolean;
{Optimised prime test - about 40% faster than the naive approach}
var I,Stop: integer;
begin
if (N = 2) or (N=3) then Result:=true
else if (n <= 1) or ((n mod 2) = 0) or ((n mod 3) = 0) then Result:= false
else
begin
I:=5;
Stop:=Trunc(sqrt(N));
Result:=False;
while I<=Stop do
begin
if ((N mod I) = 0) or ((N mod (i + 2)) = 0) then exit;
Inc(I,6);
end;
Result:=True;
end;
end;
function IsDescending(N: integer): boolean;
{Determine if each digit is less than previous, left to right}
var S: string;
var I: integer;
begin
Result:=False;
S:=IntToStr(N);
for I:=1 to Length(S)-1 do
if S[I]<=S[I+1] then exit;
Result:=True;
end;
procedure ShowDescendingPrimes(Memo: TMemo; Prog: TProgress);
{Write Descending primes up to 123,456,789 }
{The Optional progress }
var I,Cnt: integer;
var S: string;
const Max = 123456789;
begin
if Assigned(Prog) then Prog(0);
S:='';
Cnt:=0;
for I:=2 to Max do
begin
if ((I mod 1000000)=0) and Assigned(Prog) then Prog(Trunc(100*(I/Max)));
if IsDescending(I) and IsPrime(I) then
begin
S:=S+Format('%12.0n', [I*1.0]);
Inc(Cnt);
if (Cnt mod 8)=0 then
begin
Memo.Lines.Add(S);
S:='';
end;
end;
end;
if S<>'' then Memo.Lines.Add(S);
Memo.Lines.Add('Descending Primes Found: '+IntToStr(Cnt));
end;

3
Task/Descending-primes/F-Sharp/descending-primes.fs Normal file
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// Descending primes. Nigel Galloway: April 19th., 2022
[2;3;5;7]::List.unfold(fun(n,i)->match n with []->None |_->let n=n|>List.map(fun(n,g)->[for n in n..9->(n+1,i*n+g)])|>List.concat in Some(n|>List.choose(fun(_,n)->if isPrime n then Some n else None),(n|>List.filter(fst>>(>)10),i*10)))([(4,3);(2,1);(8,7)],10)
|>List.concat|>List.sort|>List.iter(printf "%d "); printfn ""

6
Task/Descending-primes/Factor/descending-primes.factor Normal file
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USING: grouping grouping.extras math math.combinatorics
math.functions math.primes math.ranges prettyprint sequences
sequences.extras ;
9 1 [a,b] all-subsets [ reverse 0 [ 10^ * + ] reduce-index ]
[ prime? ] map-filter 10 "" pad-groups 10 group simple-table.

39
Task/Descending-primes/Forth/descending-primes.fth Normal file
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: is-prime? \ n -- f ; \ Fast enough for this application
DUP 1 AND IF \ n is odd
DUP 3 DO
DUP I DUP * < IF DROP -1 LEAVE THEN \ Leave loop if I**2 > n
DUP I MOD 0= IF DROP 0 LEAVE THEN \ Leave loop if n%I is zero
2 +LOOP \ iterate over odd I only
ELSE \ n is even
2 = \ Returns true if n == 2.
THEN ;
: 1digit \ -- ; \ Select and print one digit numbers which are prime
10 2 ?DO
I is-prime? IF I 9 .r THEN
LOOP ;
: 2digit \ n-bfwd digit -- ;
\ Generate and print primes where least significant digit < digit
\ n-bfwd is the base number bought foward from calls to `digits` below.
SWAP 10 * SWAP 1 ?DO
DUP I + is-prime? IF DUP I + 9 .r THEN
2 I 3 = 2* - +LOOP DROP ; \ This generates the I sequence 1 3 7 9
: digits \ #digits n-bfwd max-digit -- ;
\ Print descendimg primes with #digits digits.
2 PICK 9 > IF ." #digits must be less than 10." 2DROP DROP EXIT THEN
2 PICK 1 = IF 2DROP DROP 1digit EXIT THEN \ One digit is special simple case
2 PICK 2 = IF \ Two digit special and
SWAP 10 * SWAP 2 DO \ I is 2 .. max-digit-1
DUP I + I 2digit
LOOP 2DROP
ELSE
SWAP 10 * SWAP 2 PICK ?DO \ I is #digits .. max-digit-1
DUP I + 2 PICK 1- SWAP I RECURSE \ Recurse with #digits reduced by 1.
LOOP 2DROP
THEN ;
: descending-primes
\ Print the descending primes. Call digits with increasing #digits
CR 9 1 DO I 0 10 digits LOOP ;

31
Task/Descending-primes/FreeBASIC/descending-primes.basic Normal file
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#include "isprime.bas"
#include "sort.bas"
Dim As Double t0 = Timer
Dim As Integer i, n, tmp, num, cant
Dim Shared As Integer matriz(512)
For i = 0 To 511
n = 0
tmp = i
num = 9
While tmp
If tmp And 1 Then n = n * 10 + num
tmp = tmp Shr 1
num -= 1
Wend
matriz(i) = n
Next i
Sort(matriz())
cant = 0
For i = 1 To Ubound(matriz)-1
n = matriz(i)
If IsPrime(n) Then
Print Using "#########"; n;
cant += 1
If cant Mod 10 = 0 Then Print
End If
Next i
Print Using !"\n\nThere are & descending primes."; cant
Sleep

63
Task/Descending-primes/Go/descending-primes.go Normal file
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package main
import (
"fmt"
"rcu"
"sort"
"strconv"
)
func combinations(a []int, k int) [][]int {
n := len(a)
c := make([]int, k)
var combs [][]int
var combine func(start, end, index int)
combine = func(start, end, index int) {
if index == k {
t := make([]int, len(c))
copy(t, c)
combs = append(combs, t)
return
}
for i := start; i <= end && end-i+1 >= k-index; i++ {
c[index] = a[i]
combine(i+1, end, index+1)
}
}
combine(0, n-1, 0)
return combs
}
func powerset(a []int) (res [][]int) {
if len(a) == 0 {
return
}
for i := 1; i <= len(a); i++ {
res = append(res, combinations(a, i)...)
}
return
}
func main() {
ps := powerset([]int{9, 8, 7, 6, 5, 4, 3, 2, 1})
var descPrimes []int
for i := 1; i < len(ps); i++ {
s := ""
for _, e := range ps[i] {
s += string(e + '0')
}
p, _ := strconv.Atoi(s)
if rcu.IsPrime(p) {
descPrimes = append(descPrimes, p)
}
}
sort.Ints(descPrimes)
fmt.Println("There are", len(descPrimes), "descending primes, namely:")
for i := 0; i < len(descPrimes); i++ {
fmt.Printf("%8d ", descPrimes[i])
if (i+1)%10 == 0 {
fmt.Println()
}
}
fmt.Println()
}

5
Task/Descending-primes/J/descending-primes.j Normal file
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extend=: {{ y;y,L:0(1+each i.1-{:y)}}
($~ q:@$)(#~ 1 p: ])10#.&>([:~.@;extend each)^:# >:i.9
2 3 31 43 41 431 421 5 53 541 521 5431 61 653 643 641 631 6521 6421 7 73 71 761 751 743 7643 7621 7541 7321
76543 76541 76421 75431 764321 83 863 853 821 8761 8753 8741 8731 8641 8543 8521 8431 87643 87641 87631 87541 87421 86531 876431 865321 8765321 8764321 97 983
971 953 941 9871 9851 9743 9721 9643 9631 9521 9431 9421 98731 98641 98621 98543 98321 97651 96431 94321 987631 987541 986543 975421 9875321 9754321 98765431 98764321 97654321

25
Task/Descending-primes/Jq/descending-primes-1.jq Normal file
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# Output: a stream of the powersets of the input array
def powersets:
if length == 0 then .
else .[-1] as $x
| .[:-1] | powersets
| ., . + [$x]
end;
def is_prime:
. as $n
| if ($n < 2) then false
elif ($n % 2 == 0) then $n == 2
elif ($n % 3 == 0) then $n == 3
elif ($n % 5 == 0) then $n == 5
elif ($n % 7 == 0) then $n == 7
elif ($n % 11 == 0) then $n == 11
elif ($n % 13 == 0) then $n == 13
elif ($n % 17 == 0) then $n == 17
elif ($n % 19 == 0) then $n == 19
else 23
| until( (. * .) > $n or ($n % . == 0); .+2)
| . * . > $n
end;
def lpad($len): tostring | ($len - length) as $l | (" " * $l)[:$l] + .;

11
Task/Descending-primes/Jq/descending-primes-2.jq Normal file
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[range(9;0;-1)]
| [powersets
| map(tostring)
| join("")
| select(length > 0)
| tonumber
| select(is_prime)]
| sort
| _nwise(10)
| map(lpad(9))
| join(" ")

9
Task/Descending-primes/Julia/descending-primes.julia Normal file
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using Combinatorics
using Primes
function descendingprimes()
return sort!(filter(isprime, [evalpoly(10, x)
for x in powerset([1, 2, 3, 4, 5, 6, 7, 8, 9]) if !isempty(x)]))
end
foreach(p -> print(rpad(p[2], 10), p[1] % 10 == 0 ? "\n" : ""), enumerate(descendingprimes()))

24
Task/Descending-primes/Lua/descending-primes.lua Normal file
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local function is_prime(n)
if n < 2 then return false end
if n % 2 == 0 then return n==2 end
if n % 3 == 0 then return n==3 end
for f = 5, n^0.5, 6 do
if n%f==0 or n%(f+2)==0 then return false end
end
return true
end
local function descending_primes()
local digits, candidates, primes = {9,8,7,6,5,4,3,2,1}, {0}, {}
for i = 1, #digits do
for j = 1, #candidates do
local value = candidates[j] * 10 + digits[i]
if is_prime(value) then primes[#primes+1] = value end
candidates[#candidates+1] = value
end
end
table.sort(primes)
return primes
end
print(table.concat(descending_primes(), ", "))

1
Task/Descending-primes/Mathematica/descending-primes.math Normal file
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Sort[Select[FromDigits/@Subsets[Range[9,1,-1],{1,\[Infinity]}],PrimeQ]]

40
Task/Descending-primes/Nim/descending-primes.nim Normal file
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import std/[strutils, sugar]
proc isPrime(n: int): bool =
assert n > 7
if n mod 2 == 0 or n mod 3 == 0: return false
var d = 5
var step = 2
while d * d <= n:
if n mod d == 0:
return false
inc d, step
step = 6 - step
result = true
iterator descendingPrimes(): int =
# Yield one digit primes.
for n in [2, 3, 5, 7]:
yield n
# Yield other primes by increasing length and in ascending order.
type Item = tuple[val, lastDigit: int]
var items: seq[Item] = collect(for n in 1..9: (n, n))
for ndigits in 2..9:
var nextItems: seq[Item]
for item in items:
for newDigit in 0..(item.lastDigit - 1):
let newVal = 10 * item.val + newDigit
nextItems.add (val: newVal, lastDigit: newDigit)
if newVal.isPrime():
yield newVal
items = move(nextItems)
var rank = 0
for prime in descendingPrimes():
inc rank
stdout.write ($prime).align(8)
stdout.write if rank mod 8 == 0: '\n' else: ' '
echo()

10
Task/Descending-primes/Perl/descending-primes.pl Normal file
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use strict;
use warnings;
use ntheory 'is_prime';
print join( '',
sort
map { sprintf '%9d', $_ }
grep /./ && is_prime $_,
glob join '', map "{$_,}", reverse 1..9
) =~ s/.{45}\K/\n/gr;

16
Task/Descending-primes/Phix/descending-primes-1.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;">function</span> <span style="color: #000000;">descending_primes</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">max_digit</span><span style="color: #0000FF;">=</span><span style="color: #000000;">9</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">max_digit</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">np</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">*</span><span style="color: #000000;">10</span><span style="color: #0000FF;">+</span><span style="color: #000000;">d</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">odd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">is_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">np</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">np</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">descending_primes</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">np</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</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;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sort</span><span style="color: #0000FF;">(</span><span style="color: #000000;">descending_primes</span><span style="color: #0000FF;">({</span><span style="color: #000000;">2</span><span style="color: #0000FF;">})),</span>
<span style="color: #000080;font-style:italic;">--sequence r = descending_primes({2}),</span>
<span style="color: #000000;">j</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">join_by</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">11</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%8d"</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;">"There are %,d descending primes:\n%s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">),</span><span style="color: #000000;">j</span><span style="color: #0000FF;">})</span>
<!--

22
Task/Descending-primes/Phix/descending-primes-2.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;">function</span> <span style="color: #000000;">descending_primes</span><span style="color: #0000FF;">()</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">powerset</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">9</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #008080;">while</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">powerset</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">filter</span><span style="color: #0000FF;">(</span><span style="color: #000000;">powerset</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">is_prime</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">next</span> <span style="color: #0000FF;">=</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: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">powerset</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">powerset</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</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: #008080;">do</span>
<span style="color: #000000;">next</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">powerset</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">10</span><span style="color: #0000FF;">+</span><span style="color: #000000;">d</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">powerset</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">next</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">descending_primes</span><span style="color: #0000FF;">(),</span>
<span style="color: #000000;">j</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">join_by</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">11</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%8d"</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;">"There are %,d descending primes:\n%s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">),</span><span style="color: #000000;">j</span><span style="color: #0000FF;">})</span>
<!--

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Task/Descending-primes/Picat/descending-primes.picat Normal file
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import util.
main =>
DP = [N : S in power_set("987654321"), S != [], N = S.to_int, prime(N)].sort,
foreach({P,I} in zip(DP,1..DP.len))
printf("%9d%s",P,cond(I mod 10 == 0,"\n",""))
end,
nl,
println(len=DP.len).

11
Task/Descending-primes/Python/descending-primes.py Normal file
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from sympy import isprime
def descending(xs=range(10)):
for x in xs:
yield x
yield from descending(x*10 + d for d in range(x%10))
for i, p in enumerate(sorted(filter(isprime, descending()))):
print(f'{p:9d}', end=' ' if (1 + i)%8 else '\n')
print()

9
Task/Descending-primes/Quackery/descending-primes.quackery Normal file
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[ 0 swap witheach
[ swap 10 * + ] ] is digits->n ( [ --> n )
[]
' [ 9 8 7 6 5 4 3 2 1 ] powerset
witheach
[ digits->n dup isprime
iff join else drop ]
sort echo

6
Task/Descending-primes/Raku/descending-primes.raku Normal file
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put (flat 2, 3, 5, 7, sort +*, gather (3..9).map: &recurse ).batch(10)».fmt("%8d").join: "\n";
sub recurse ($str) {
.take for ($str X~ (1, 3, 7)).grep: { .is-prime && [>] .comb };
recurse $str × 10 + $_ for 2 ..^ $str % 10;
}

40
Task/Descending-primes/Ring/descending-primes.ring Normal file
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show("decending primes", sort(cending_primes(seq(9, 1))))
func show(title, itm)
l = len(itm); ? "" + l + " " + title + ":"
for i = 1 to l
see fmt(itm[i], 9)
if i % 5 = 0 and i < l? "" ok
next : ? ""
func seq(b, e)
res = []; d = e - b
s = d / fabs(d)
for i = b to e step s add(res, i) next
return res
func ispr(n)
if n < 2 return 0 ok
if n & 1 = 0 return n = 2 ok
if n % 3 = 0 return n = 3 ok
l = sqrt(n)
for f = 5 to l
if n % f = 0 or n % (f + 2) = 0 return false ok
next : return 1
func cending_primes(digs)
cand = [0]
pr = []
for i in digs
lcand = cand
for j in lcand
v = j * 10 + i
if ispr(v) add(pr, v) ok
add(cand, v)
next
next
return pr
func fmt(x, l)
res = " " + x
return right(res, l)

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Task/Descending-primes/Ruby/descending-primes.rb Normal file
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require 'prime'
digits = [9,8,7,6,5,4,3,2,1].to_a
res = 1.upto(digits.size).flat_map do |n|
digits.combination(n).filter_map do |set|
candidate = set.join.to_i
candidate if candidate.prime?
end.reverse
end
puts res.join(",")

30
Task/Descending-primes/Sidef/descending-primes.sidef Normal file
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func primes_with_descending_digits(base = 10) {
var list = []
var digits = @(1..^base)
var end_digits = digits.grep { .is_coprime(base) }
list << digits.grep { .is_prime && !.is_coprime(base) }...
for k in (0 .. digits.end) {
digits.combinations(k, {|*a|
var v = a.digits2num(base)
end_digits.each {|d|
var n = (v*base + d)
next if ((n >= base) && (a[0] <= d))
list << n if n.is_prime
}
})
}
list.sort
}
var base = 10
var arr = primes_with_descending_digits(base)
say "There are #{arr.len} descending primes in base #{base}.\n"
arr.each_slice(8, {|*a|
say a.map { '%9s' % _ }.join(' ')
})

12
Task/Descending-primes/Wren/descending-primes.wren Normal file
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import "./perm" for Powerset
import "./math" for Int
import "./seq" for Lst
import "./fmt" for Fmt
var ps = Powerset.list((9..1).toList)
var descPrimes = ps.skip(1).map { |s| Num.fromString(s.join()) }
.where { |p| Int.isPrime(p) }
.toList
.sort()
System.print("There are %(descPrimes.count) descending primes, namely:")
for (chunk in Lst.chunks(descPrimes, 10)) Fmt.print("$8s", chunk)

25
Task/Descending-primes/XPL0/descending-primes.xpl0 Normal file
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include xpllib; \provides IsPrime and Sort
int I, N, Mask, Digit, A(512), Cnt;
[for I:= 0 to 511 do
[N:= 0; Mask:= I; Digit:= 9;
while Mask do
[if Mask&1 then
N:= N*10 + Digit;
Mask:= Mask>>1;
Digit:= Digit-1;
];
A(I):= N;
];
Sort(A, 512);
Cnt:= 0;
Format(9, 0);
for I:= 1 to 511 do \skip empty set
[N:= A(I);
if IsPrime(N) then
[RlOut(0, float(N));
Cnt:= Cnt+1;
if rem(Cnt/10) = 0 then CrLf(0);
];
];
]