# Ascending primes

Ascending primes
You are encouraged to solve this task according to the task description, using any language you may know.

Generate and show all primes with strictly ascending decimal digits.

Aside: Try solving without peeking at existing solutions. I had a weird idea for generating a prime sieve faster, which needless to say didn't pan out. The solution may be p(r)etty trivial but generating them quickly is at least mildly interesting. Tip: filtering all 7,027,260 primes below 123,456,789 probably won't kill you, but there is at least one significantly better and much faster way, needing a mere 511 odd/prime tests.

Related

## 11l

Translation of: Python
```F isprime(n)
I n == 2
R 1B
I n == 1 | n % 2 == 0
R 0B
V root1 = Int(n ^ 0.5) + 1
L(k) (3 .< root1).step(2)
I n % k == 0
R 0B
R 1B

V queue = Array(1..9)
[Int] primes

L !queue.empty
V n = queue.pop(0)
I isprime(n)
primes.append(n)
queue.extend((n % 10 + 1 .< 10).map(k -> @n * 10 + k))

print(primes)```
Output:
```[2, 3, 5, 7, 13, 17, 19, 23, 29, 37, 47, 59, 67, 79, 89, 127, 137, 139, 149, 157, 167, 179, 239, 257, 269, 347, 349, 359, 367, 379, 389, 457, 467, 479, 569, 1237, 1249, 1259, 1279, 1289, 1367, 1459, 1489, 1567, 1579, 1789, 2347, 2357, 2389, 2459, 2467, 2579, 2689, 2789, 3457, 3467, 3469, 4567, 4679, 4789, 5689, 12347, 12379, 12457, 12479, 12569, 12589, 12689, 13457, 13469, 13567, 13679, 13789, 15679, 23459, 23567, 23689, 23789, 25679, 34589, 34679, 123457, 123479, 124567, 124679, 125789, 134789, 145679, 234589, 235679, 235789, 245789, 345679, 345689, 1234789, 1235789, 1245689, 1456789, 12356789, 23456789]
```

## ALGOL 68

Uses Pete's hint to enumerate the 512 possible numbers.
The numbers are generated in order of the first digit, so we have to sort them. As there are only 512 possible numbers to consider, it doesn't attempt the optimisation that the final digit can't be 4, 6 or 8 and can only be 2 or 5 if it is the only digit (also, I always forget that can't be even thing...).

Works with: ALGOL 68G version Any - tested with release 2.8.3.win32
Library: ALGOL 68-rows
```BEGIN # find all primes with strictly increasing 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 = d1;
FOR d2 FROM 0 TO 1 DO
INT n2 = IF d2 = 1 THEN ( n1 * 10 ) + 2 ELSE n1 FI;
FOR d3 FROM 0 TO 1 DO
INT n3 = IF d3 = 1 THEN ( n2 * 10 ) + 3 ELSE n2 FI;
FOR d4 FROM 0 TO 1 DO
INT n4 = IF d4 = 1 THEN ( n3 * 10 ) + 4 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 ) + 6 ELSE n5 FI;
FOR d7 FROM 0 TO 1 DO
INT n7 = IF d7 = 1 THEN ( n6 * 10 ) + 7 ELSE n6 FI;
FOR d8 FROM 0 TO 1 DO
INT n8 = IF d8 = 1 THEN ( n7 * 10 ) + 8 ELSE n7 FI;
FOR d9 FROM 0 TO 1 DO
INT n9 = IF d9 = 1 THEN ( n8 * 10 ) + 9 ELSE n8 FI;
IF n9 > 0 THEN
IF is probably prime( n9 ) THEN
# have a prime with strictly ascending 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 #
FOR i TO p count DO                                # display the primes #
print( ( "  ", whole( primes[ i ], -8 ) ) );
IF i MOD 10 = 0 THEN print( ( newline ) ) FI
OD
END```
Output:
```         2         3         5         7        13        17        19        23        29        37
47        59        67        79        89       127       137       139       149       157
167       179       239       257       269       347       349       359       367       379
389       457       467       479       569      1237      1249      1259      1279      1289
1367      1459      1489      1567      1579      1789      2347      2357      2389      2459
2467      2579      2689      2789      3457      3467      3469      4567      4679      4789
5689     12347     12379     12457     12479     12569     12589     12689     13457     13469
13567     13679     13789     15679     23459     23567     23689     23789     25679     34589
34679    123457    123479    124567    124679    125789    134789    145679    234589    235679
235789    245789    345679    345689   1234789   1235789   1245689   1456789  12356789  23456789
```

## ALGOL W

Translation of: Lua

...and only a few characters different from the Algol W Descending primes sample.

```begin % find all primes with strictly ascending digits - translation of Lua  %

% quicksorts v, the bounds of v must be specified in lb and ub           %
procedure quicksort ( integer array v( * )
; integer value lb, ub
) ;
if ub > lb then begin
% more than one element, so must sort %
integer left, right, pivot;
left   := lb;
right  := ub;
% choosing the middle element of the array as the pivot %
pivot  := v( left + ( ( right + 1 ) - left ) div 2 );
while begin
while left  <= ub and v( left  ) < pivot do left  := left  + 1;
while right >= lb and v( right ) > pivot do right := right - 1;
left <= right
end do begin
integer swap;
swap       := v( left  );
v( left  ) := v( right );
v( right ) := swap;
left       := left  + 1;
right      := right - 1
end while_left_le_right ;
quicksort( v, lb,   right );
quicksort( v, left, ub    )
end quicksort ;

% returns true if n is prime, false otherwise                            %
logical procedure is_prime( integer value n ) ;
if      n  <  2     then false
else if n rem 2 = 0 then n = 2
else if n rem 3 = 0 then n = 3
else begin
logical prime; prime := true;
for f := 5 step 6 until entier( sqrt( n ) ) do begin
if n rem f = 0 or n rem ( f + 2 ) = 0 then begin
prime := false;
goto done
end if_n_rem_f_eq_0_or_n_rem_f_plus_2_eq_0
end for_f;
done:       prime
end is_prime ;

% increments n and also returns its new value                            %
integer procedure inc ( integer value result n ) ; begin n := n + 1; n end;

% sets primes to the list of ascending primes and lenPrimes to the       %
% number of ascending primes - primes must be big enough, e.g. have 511  %
% elements                                                               %
procedure ascending_primes ( integer array primes ( * )
; integer result lenPrimes
) ;
begin
integer array digits     ( 1 ::    9 );
integer array candidates ( 1 :: 6000 );
integer lenCandidates;
candidates( 1 ) := 0;
lenCandidates   := 1;
lenPrimes       := 0;
for i := 1 until 9 do digits( i ) := i;
for i := 1 until 9 do begin
for j := 1 until lenCandidates do begin
integer cValue; cValue := candidates( j ) * 10 + digits( i );
if is_prime( cValue ) then primes( inc( lenPrimes ) ) := cValue;
candidates( inc( lenCandidates ) ) := cValue
end for_j
end for_i ;
quickSort( primes, 1, lenPrimes );
end ascending_primes ;

begin % find the ascending primes and print them                         %
integer array primes ( 1 :: 512 );
integer lenPrimes;
ascending_primes( primes, lenPrimes );
for i := 1 until lenPrimes do begin
writeon( i_w := 8, s_w := 0, " ", primes( i ) );
if i rem 10 = 0 then write()
end for_i
end
end.```
Output:
```        2        3        5        7       13       17       19       23       29       37
47       59       67       79       89      127      137      139      149      157
167      179      239      257      269      347      349      359      367      379
389      457      467      479      569     1237     1249     1259     1279     1289
1367     1459     1489     1567     1579     1789     2347     2357     2389     2459
2467     2579     2689     2789     3457     3467     3469     4567     4679     4789
5689    12347    12379    12457    12479    12569    12589    12689    13457    13469
13567    13679    13789    15679    23459    23567    23689    23789    25679    34589
34679   123457   123479   124567   124679   125789   134789   145679   234589   235679
235789   245789   345679   345689  1234789  1235789  1245689  1456789 12356789 23456789
```

## Arturo

```ascending?: function [x][
initial: digits x
and? [equal? sort initial initial][equal? size initial size unique initial]
]

candidates: select (1..1456789) ++ [
12345678, 12345679, 12345689, 12345789, 12346789,
12356789, 12456789, 13456789, 23456789, 123456789
] => prime?

ascendingNums: select candidates => ascending?

loop split.every:10 ascendingNums 'nums [
print map nums 'num -> pad to :string num 10
]
```
Output:
```         2          3          5          7         13         17         19         23         29         37
47         59         67         79         89        127        137        139        149        157
167        179        239        257        269        347        349        359        367        379
389        457        467        479        569       1237       1249       1259       1279       1289
1367       1459       1489       1567       1579       1789       2347       2357       2389       2459
2467       2579       2689       2789       3457       3467       3469       4567       4679       4789
5689      12347      12379      12457      12479      12569      12589      12689      13457      13469
13567      13679      13789      15679      23459      23567      23689      23789      25679      34589
34679     123457     123479     124567     124679     125789     134789     145679     234589     235679
235789     245789     345679     345689    1234789    1235789    1245689    1456789   12356789   23456789```

## AWK

```# syntax: GAWK -f ASCENDING_PRIMES.AWK
BEGIN {
start = 1
stop = 23456789
for (i=start; i<=stop; i++) {
if (is_prime(i)) {
primes++
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) {
printf("%9d%1s",i,++count%10?"":"\n")
}
}
}
printf("\n%d-%d: %d primes, %d ascending primes\n",start,stop,primes,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)
}
```
Output:
```        2         3         5         7        13        17        19        23        29        37
47        59        67        79        89       127       137       139       149       157
167       179       239       257       269       347       349       359       367       379
389       457       467       479       569      1237      1249      1259      1279      1289
1367      1459      1489      1567      1579      1789      2347      2357      2389      2459
2467      2579      2689      2789      3457      3467      3469      4567      4679      4789
5689     12347     12379     12457     12479     12569     12589     12689     13457     13469
13567     13679     13789     15679     23459     23567     23689     23789     25679     34589
34679    123457    123479    124567    124679    125789    134789    145679    234589    235679
235789    245789    345679    345689   1234789   1235789   1245689   1456789  12356789  23456789

1-23456789: 1475171 primes, 100 ascending primes
```

## C

Translation of: Fortran
```/*
*  Ascending primes
*
*  Generate and show all primes with strictly ascending decimal digits.
*
*
*  Solution
*
*  We only consider positive numbers in the range 1 to 123456789. We would
*  get 7027260 primes, because there are so many primes smaller than 123456789
*  (see also Wolfram Alpha).On the other hand, there are only 511 distinct
*  nonzero positive integers having their digits arranged in ascending order.
*  Therefore, it is better to start with numbers that have properly arranged
*  digitsand then check if they are prime numbers.The method of generating
*  a sequence of such numbers is not indifferent.We want this sequence to be
*  monotonically increasing, because then additional sorting of results will
*  be unnecessary. It turns out that by using a queue we can easily get the
*  desired effect. Additionally, the algorithm then does not use recursion
*  (although the program probably does not have to comply with the MISRA
*  standard). The problem to be solved is the queue size, the a priori
*  assumption that 1000 is good enough, but a bit magical.
*/

#include <stdio.h>
#include <stdlib.h>
#include <stdbool.h>
#include <math.h>

#if UINT_MAX < 123456789
#error "we need at least 9 decimal digits (32-bit integers)"
#endif

#define MAXSIZE 1000

unsigned queue[MAXSIZE];
unsigned primes[MAXSIZE];

unsigned begin = 0;
unsigned end = 0;
unsigned n = 0;

bool isPrime(unsigned n)
{
if (n == 2)
{
return true;
}
if (n == 1 || n % 2 == 0)
{
return false;
}
unsigned root = sqrt(n);
for (unsigned k = 3; k <= root; k += 2)
{
if (n % k == 0)
{
return false;
}
}
return true;
}

int main(int argc, char argv[])
{
for (int k = 1; k <= 9; k++)
{
queue[end++] = k;
}

while (begin < end)
{
int value = queue[begin++];
if (isPrime(value))
{
primes[n++] = value;
}
for (int k = value % 10 + 1; k <= 9; k++)
{
queue[end++] = value * 10 + k;
}
}

for (int k = 0; k < n; k++)
{
printf("%u ", primes[k]);
}

return EXIT_SUCCESS;
}
```
Output:
`2 3 5 7 13 17 19 23 29 37 47 59 67 79 89 127 137 139 149 157 167 179 239 257 269 347 349 359 367 379 389 457 467 479 569 1237 1249 1259 1279 1289 1367 1459 1489 1567 1579 1789 2347 2357 2389 2459 2467 2579 2689 2789 3457 3467 3469 4567 4679 4789 5689 12347 12379 12457 12479 12569 12589 12689 13457 13469 13567 13679 13789 15679 23459 23567 23689 23789 25679 34589 34679 123457 123479 124567 124679 125789 134789 145679 234589 235679 235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789 `

## C++

Translation of: C
```/*
*  Ascending primes
*
*  Generate and show all primes with strictly ascending decimal digits.
*
*
*  Solution
*
*  We only consider positive numbers in the range 1 to 123456789. We would
*  get 7027260 primes, because there are so many primes smaller than 123456789
*  (see also Wolfram Alpha).On the other hand, there are only 511 distinct
*  nonzero positive integers having their digits arranged in ascending order.
*  Therefore, it is better to start with numbers that have properly arranged
*  digitsand then check if they are prime numbers.The method of generating
*  a sequence of such numbers is not indifferent.We want this sequence to be
*  monotonically increasing, because then additional sorting of results will
*  be unnecessary. It turns out that by using a queue we can easily get the
*  desired effect. Additionally, the algorithm then does not use recursion
*  (although the program probably does not have to comply with the MISRA
*  standard). The problem to be solved is the queue size, the a priori
*  assumption that 1000 is good enough, but a bit magical.
*/

#include <cmath>
#include <iostream>
#include <queue>
#include <vector>

using namespace std;

queue<unsigned> suspected;
vector<unsigned> primes;

bool isPrime(unsigned n)
{
if (n == 2)
{
return true;
}
if (n == 1 || n % 2 == 0)
{
return false;
}
unsigned root = sqrt(n);
for (unsigned k = 3; k <= root; k += 2)
{
if (n % k == 0)
{
return false;
}
}
return true;
}

int main(int argc, char argv[])
{
for (unsigned k = 1; k <= 9; k++)
{
suspected.push(k);
}

while (!suspected.empty())
{
int n = suspected.front();
suspected.pop();

if (isPrime(n))
{
primes.push_back(n);
}

//  The value of n % 10 gives the least significient digit of n
//
for (unsigned k = n % 10 + 1; k <= 9; k++)
{
suspected.push(n * 10 + k);
}
}

copy(primes.begin(), primes.end(), ostream_iterator<unsigned>(cout, " "));

return EXIT_SUCCESS;
}
```
Output:
`2 3 5 7 13 17 19 23 29 37 47 59 67 79 89 127 137 139 149 157 167 179 239 257 269 347 349 359 367 379 389 457 467 479 569 1237 1249 1259 1279 1289 1367 1459 1489 1567 1579 1789 2347 2357 2389 2459 2467 2579 2689 2789 3457 3467 3469 4567 4679 4789 5689 12347 12379 12457 12479 12569 12589 12689 13457 13469 13567 13679 13789 15679 23459 23567 23689 23789 25679 34589 34679 123457 123479 124567 124679 125789 134789 145679 234589 235679 235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789 `

## C#

Translation of: PHP
```using System;
using System.Collections.Generic;

namespace ascendingprimes
{
class Program
{
static bool isPrime(uint n)
{
if (n == 2)
return true;
if (n == 1 || n % 2 = 0)
return false;
uint root = (uint)Math.Sqrt(n);
for (uint k = 3; k <= root; k += 2)
if (n % k == 0)
return false;
return true;
}
static void Main(string[] args)
{
var queue = new Queue<uint>();
var primes = new List<uint>();

for (uint k = 1; k <= 9; k++)
queue.Enqueue(k);
while(queue.Count > 0)
{
uint n = queue.Dequeue();
if (isPrime(n))
for (uint k = n % 10 + 1; k <= 9; k++)
queue.Enqueue(n * 10 + k);
}

foreach (uint p in primes)
{
Console.Write(p);
Console.Write(" ");
}
Console.WriteLine();
}
}
}
```
Output:
`2 3 5 7 13 17 19 23 29 37 47 59 67 79 89 127 137 139 149 157 167 179 239 257 269 347 349 359 367 379 389 457 467 479 569 1237 1249 1259 1279 1289 1367 1459 1489 1567 1579 1789 2347 2357 2389 2459 2467 2579 2689 2789 3457 3467 3469 4567 4679 4789 5689 12347 12379 12457 12479 12569 12589 12689 13457 13469 13567 13679 13789 15679 23459 23567 23689 23789 25679 34589 34679 123457 123479 124567 124679 125789 134789 145679 234589 235679 235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789`

## Delphi

Works with: Delphi version 6.0
```uses Windows,SysUtils,StdCtrls;

type TProgress = procedure(Percent: integer);

procedure ShowAscendingPrimes(Memo: TMemo; Prog: TProgress);

implementation

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 IsAscending(N: integer): boolean;
{Determine if each digit is greater 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 ShowAscendingPrimes(Memo: TMemo; Prog: TProgress);
{Write Ascending primes up to 123,456,789 }
{It has an optional, user-supplied progress routine }
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 IsAscending(I) and IsPrime(I) then
begin
S:=S+Format('%9.0d', [I]);
Inc(Cnt);
if (Cnt mod 10)=0 then
begin
S:='';
end;
end;
end;
end;
```
Output:
```        2        3        5        7       13       17       19       23       29       37
47       59       67       79       89      127      137      139      149      157
167      179      239      257      269      347      349      359      367      379
389      457      467      479      569     1237     1249     1259     1279     1289
1367     1459     1489     1567     1579     1789     2347     2357     2389     2459
2467     2579     2689     2789     3457     3467     3469     4567     4679     4789
5689    12347    12379    12457    12479    12569    12589    12689    13457    13469
13567    13679    13789    15679    23459    23567    23689    23789    25679    34589
34679   123457   123479   124567   124679   125789   134789   145679   234589   235679
235789   245789   345679   345689  1234789  1235789  1245689  1456789 12356789 23456789
```

## Dylan

Translation of: C++
```define function prime? (n :: <integer>) => (p :: <boolean>)
case
n == 2
=> #t;
n == 1 | remainder(n, 2) == 0
=> #f;
otherwise
=> let root = sqrt(as(<double-float>, n));
iterate loop (k = 3)
case
remainder(n, k) == 0 => #f;
k > root             => #t;
otherwise            => loop(k + 2);
end
end
end case
end function;

define function ascending-primes () => (primes :: <sequence>)
let maybe = make(<deque>);
for (k from 1 to 9)
push-last(maybe, k)
end;
let primes = make(<stretchy-vector>);
while (~empty?(maybe))
let n = pop(maybe);
if (prime?(n))
end;
for (k from modulo(n, 10) + 1 to 9)
push-last(maybe, n * 10 + k)
end
end;
primes
end function;

format-out("%=", ascending-primes());
```
Output:
`{stretchy vector 2, 5, 7, 13, 17, 19, 23, 29, 37, 47, 59, 67, 79, 89, 127, 137, 139, 149, 157, 167, 179, 239, 257, 269, 347, 349, 359, 367, 379, 389, 457, 467, 479, 569, 1237, 1249, 1259, 1279, 1289, 1367, 1459, 1489, 1567, 1579, 1789, 2347, 2357, 2389, 2459, 2467, 2579, 2689, 2789, 3457, 3467, 3469, 4567, 4679, 4789, 5689, 12347, 12379, 12457, 12479, 12569, 12589, 12689, 13457, 13469, 13567, 13679, 13789, 15679, 23459, 23567, 23689, 23789, 25679, 34589, 34679, 123457, 123479, 124567, 124679, 125789, 134789, 145679, 234589, 235679, 235789, 245789, 345679, 345689, 1234789, 1235789, 1245689, 1456789, 12356789, 23456789}`

## EasyLang

This outputs all 100 ascending primes. They are not sorted - that was not demanded anyway.

```func isprim num .
if num < 2
return 0
.
i = 2
while i <= sqrt num
if num mod i = 0
return 0
.
i += 1
.
return 1
.
proc nextasc n . .
if isprim n = 1
write n & " "
.
if n > 123456789
return
.
for d = n mod 10 + 1 to 9
nextasc n * 10 + d
.
.
nextasc 0```

## F#

This task uses Extensible Prime Generator (F#)

```// Ascending 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.. -1..1->(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>>(<)0),i*10)))([(2,3);(6,7);(8,9)],10)
|>List.concat|>List.sort|>List.iter(printf "%d "); printfn ""
```
Output:
```2 3 5 7 13 17 19 23 29 37 47 59 67 79 89 127 137 139 149 157 167 179 239 257 269 347 349 359 367 379 389 457 467 479 569 1237 1249 1259 1279 1289 1367 1459 1489 1567 1579 1789 2347 2357 2389 2459 2467 2579 2689 2789 3457 3467 3469 4567 4679 4789 5689 12347 12379 12457 12479 12569 12589 12689 13457 13469 13567 13679 13789 15679 23459 23567 23689 23789 25679 34589 34679 123457 123479 124567 124679 125789 134789 145679 234589 235679 235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789
```

## Factor

The approach taken is to check the members of the powerset of [1..9] (of which there are only 512 if you include the empty set) for primality.

Works with: Factor version 0.99 2021-06-02
```USING: grouping math math.combinatorics math.functions
math.primes math.ranges prettyprint sequences sequences.extras ;

9 [1,b] all-subsets [ reverse 0 [ 10^ * + ] reduce-index ]
[ prime? ] map-filter 10 group simple-table.
```
Output:
```2      3      5      7      13      17      19      23      29       37
47     59     67     79     89      127     137     139     149      157
167    179    239    257    269     347     349     359     367      379
389    457    467    479    569     1237    1249    1259    1279     1289
1367   1459   1489   1567   1579    1789    2347    2357    2389     2459
2467   2579   2689   2789   3457    3467    3469    4567    4679     4789
5689   12347  12379  12457  12479   12569   12589   12689   13457    13469
13567  13679  13789  15679  23459   23567   23689   23789   25679    34589
34679  123457 123479 124567 124679  125789  134789  145679  234589   235679
235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789
```

## Forth

Works with: gforth version 0.7.3

```#! /usr/bin/gforth

\ Ascending primes

\ checks (by simple trial-division) whether the TOS is prime
: prime? ( n -- f )
dup 1 <= IF
drop false
ELSE
dup 2 = IF
drop true
ELSE
2
BEGIN
2dup dup * > >r
2dup mod 0> r>
over and
WHILE
drop 1+
REPEAT
nip nip
THEN
THEN
;

: ascending-primes-aux ( n i -- )
dup 10 = IF
drop
dup prime? IF
.
ELSE
drop
THEN
ELSE
2dup 1+ recurse                  \ do not include digit i
swap 10 * over + swap 1+ recurse \ do include digit i
THEN
;

\ prints all primes with strictly ascending digits
: ascending-primes ( -- )
0 1 ascending-primes-aux cr
;

ascending-primes bye
```
Output:
```./ascending-primes.fs
89 7 79 67 5 59 569 5689 47 479 4789 467 4679 457 4567 3 389 37 379 367 359 349 347 3469 3467 34679 34589 3457 345689 345679 2 29 2789 269 2689 257 2579 25679 2467 2459 245789 23 239 2389 23789 23689 2357 235789 23567 235679 2347 23459 234589 23456789 19 17 179 1789 167 157 1579 1567 15679 149 1489 1459 145679 1456789 13 139 137 13789 1367 13679 13567 134789 13469 13457 1289 127 1279 12689 1259 12589 125789 12569 1249 12479 124679 12457 1245689 124567 1237 12379 1235789 12356789 12347 123479 1234789 123457
```

## Fortran

```! Ascending primes
!
! Generate and show all primes with strictly ascending decimal digits.
!
!
! Solution
!
! We only consider positive numbers in the range 1 to 123456789. We would get
! 7027260 primes, because there are so many primes smaller than 123456789 (see
! also Wolfram Alpha). On the other hand, there are only 511 distinct positive
! integers having their digits arranged in ascending order. Therefore, it is
! better to start with numbers that have properly arranged digits and then check
! if they are prime numbers. The method of generating a sequence of such numbers
! is not indifferent. We want this sequence to be monotonically increasing,
! because then additional sorting of results will be unnecessary. It turns out
! that by using a queue we can easily get the desired effect. Additionally, the
! algorithm then does not use recursion (although the program probably does not
! have to comply with the MISRA standard). The problem to be solved is the queue
! size, the a priori assumption that 1000 is good enough, but a bit magical.

program prog

parameter (MAXSIZE = 1000)

logical isprime
dimension iqueue(MAXSIZE)
dimension iprimes(MAXSIZE)

ibegin = 1
iend = 1
n = 0

do k = 1, 9
iqueue(iend) = k
iend = iend + 1
end do

do while (ibegin .lt. iend)
iv = iqueue(ibegin)
ibegin = ibegin + 1
if (isprime(iv)) then
n = n + 1
iprimes(n) = iv
end if
lsd1 = mod(iv, 10) + 1
if (lsd1 .le. 9) then
do k = lsd1, 9
iqueue(iend) = iv * 10 + k
iend = iend + 1
end do
end if
end do

print *, (iprimes(i), i = 1, n)

end program

logical function isprime(n)

! Slightly improved algorithm for checking if a number is prime.
! First, we check the special cases: 0, 1, 2. Then we check whether
! the number is divisible by 2. If it is not divisible by two,
! we check whether it is divisible by odd numbers not greater than
! the square root of that number.
!
! Positive numbers only. BTW, negative numbers are prime numbers
! if their absolute values are prime numbers.

isprime = .FALSE.
if (n .eq. 0 .or. n .eq. 1) then
return
end if
if (n .ne. 2) then
if (mod(n, 2) .eq. 0) then
return
end if
m = n**0.5
do k = 3, m, 2
if (mod(n, k) .eq. 0) then
return
end if
end do
end if
isprime = .TRUE.
end function
```
Output:

The estimated execution time is 1.5 milliseconds on the same hardware on which the Java program was run. It should be remembered that modern CPUs do not have a constant clock speed and additionally the measured times depend on the system load with other tasks. Nevertheless, the Fortran program seems to be 4 times faster than the Java program.

```           2           3           5           7          13          17
19          23          29          37          47          59
67          79          89         127         137         139
149         157         167         179         239         257
269         347         349         359         367         379
389         457         467         479         569        1237
1249        1259        1279        1289        1367        1459
1489        1567        1579        1789        2347        2357
2389        2459        2467        2579        2689        2789
3457        3467        3469        4567        4679        4789
5689       12347       12379       12457       12479       12569
12589       12689       13457       13469       13567       13679
13789       15679       23459       23567       23689       23789
25679       34589       34679      123457      123479      124567
124679      125789      134789      145679      234589      235679
235789      245789      345679      345689     1234789     1235789
1245689     1456789    12356789    23456789
```

## FreeBASIC

### Power Set

Translation of: XPL0
```#include "isprime.bas"
#include "sort.bas"

Dim As Integer i, n, tmp, num, cant = 0
Dim Shared As Integer matriz(512)
For i = 0 To Ubound(matriz)-1
n = 0
tmp = i
num = 1
While tmp
If tmp And 1 Then n = n * 10 + num
tmp Shr= 1
num += 1
Wend
matriz(i)= n
Next i

Sort(matriz())

For i = 1 To Ubound(matriz)-1     'skip empty set
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 !"\nThere are & ascending primes."; cant

Sleep```

Output:
```        2        3        5        7       13       17       19       23       29       37
47       59       67       79       89      127      137      139      149      157
167      179      239      257      269      347      349      359      367      379
389      457      467      479      569     1237     1249     1259     1279     1289
1367     1459     1489     1567     1579     1789     2347     2357     2389     2459
2467     2579     2689     2789     3457     3467     3469     4567     4679     4789
5689    12347    12379    12457    12479    12569    12589    12689    13457    13469
13567    13679    13789    15679    23459    23567    23689    23789    25679    34589
34679   123457   123479   124567   124679   125789   134789   145679   234589   235679
235789   245789   345679   345689  1234789  1235789  1245689  1456789 12356789 23456789

There are 100 ascending primes.```

## FutureBasic

```local fn IsPrime( n as NSUInteger ) as BOOL
BOOL       isPrime = YES
NSUInteger i

if n < 2        then exit fn = NO
if n = 2        then exit fn = YES
if n mod 2 == 0 then exit fn = NO
for i = 3 to int(n^.5) step 2
if n mod i == 0 then exit fn = NO
next
end fn = isPrime

void local fn AscendingPrimes( limit as long )
long i, n, mask, num, count = 0

for i = 0 to limit -1
n = 0 : mask = i : num = 1
if mask & 1 then n = n * 10 + num
num++
wend
mda(i) = n
next

mda_sort @"compare:"

for i = 1 to mda_count (0) - 1
n = mda_integer(i)
if ( fn IsPrime( n ) )
printf @"%10ld\b", n
count++
if count mod 10 == 0 then print
end if
next
printf @"\n\tThere are %ld ascending primes.", count
end fn

window 1, @"Ascending Primes", ( 0, 0, 780, 230 )
print

CFTimeInterval t
t = fn CACurrentMediaTime
fn AscendingPrimes( 512 )
printf @"\n\tCompute time: %.3f ms\n",(fn CACurrentMediaTime-t)*1000

HandleEvents```
Output:
```         2         3         5         7        13        17        19        23        29        37
47        59        67        79        89       127       137       139       149       157
167       179       239       257       269       347       349       359       367       379
389       457       467       479       569      1237      1249      1259      1279      1289
1367      1459      1489      1567      1579      1789      2347      2357      2389      2459
2467      2579      2689      2789      3457      3467      3469      4567      4679      4789
5689     12347     12379     12457     12479     12569     12589     12689     13457     13469
13567     13679     13789     15679     23459     23567     23689     23789     25679     34589
34679    123457    123479    124567    124679    125789    134789    145679    234589    235679
235789    245789    345679    345689   1234789   1235789   1245689   1456789  12356789  23456789

There are 100 ascending primes.

Compute time: 9.008 ms
```

## Go

Translation of: Wren
Library: Go-rcu

Using a generator.

```package main

import (
"fmt"
"rcu"
"sort"
)

var ascPrimesSet = make(map[int]bool) // avoids duplicates

func generate(first, cand, digits int) {
if digits == 0 {
if rcu.IsPrime(cand) {
ascPrimesSet[cand] = true
}
return
}
for i := first; i < 10; i++ {
next := cand*10 + i
generate(i+1, next, digits-1)
}
}

func main() {
for digits := 1; digits < 10; digits++ {
generate(1, 0, digits)
}
le := len(ascPrimesSet)
ascPrimes := make([]int, le)
i := 0
for k := range ascPrimesSet {
ascPrimes[i] = k
i++
}
sort.Ints(ascPrimes)
fmt.Println("There are", le, "ascending primes, namely:")
for i := 0; i < le; i++ {
fmt.Printf("%8d ", ascPrimes[i])
if (i+1)%10 == 0 {
fmt.Println()
}
}
}
```
Output:
```There are 100 ascending primes, namely:
2        3        5        7       13       17       19       23       29       37
47       59       67       79       89      127      137      139      149      157
167      179      239      257      269      347      349      359      367      379
389      457      467      479      569     1237     1249     1259     1279     1289
1367     1459     1489     1567     1579     1789     2347     2357     2389     2459
2467     2579     2689     2789     3457     3467     3469     4567     4679     4789
5689    12347    12379    12457    12479    12569    12589    12689    13457    13469
13567    13679    13789    15679    23459    23567    23689    23789    25679    34589
34679   123457   123479   124567   124679   125789   134789   145679   234589   235679
235789   245789   345679   345689  1234789  1235789  1245689  1456789 12356789 23456789
```

## J

Compare with Descending primes.

```_10 ]\ /:~ (#~ 1&p:) 10&#.@I. #: i. 513
```
Output:
```     2      3      5      7      13      17      19      23       29       37
47     59     67     79      89     127     137     139      149      157
167    179    239    257     269     347     349     359      367      379
389    457    467    479     569    1237    1249    1259     1279     1289
1367   1459   1489   1567    1579    1789    2347    2357     2389     2459
2467   2579   2689   2789    3457    3467    3469    4567     4679     4789
5689  12347  12379  12457   12479   12569   12589   12689    13457    13469
13567  13679  13789  15679   23459   23567   23689   23789    25679    34589
34679 123457 123479 124567  124679  125789  134789  145679   234589   235679
235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789
```

## Java

Translation of: C++
```/*
*  Ascending primes
*
*  Generate and show all primes with strictly ascending decimal digits.
*
*
*  Solution
*
*  We only consider positive numbers in the range 1 to 123456789. We would
*  get 7027260 primes, because there are so many primes smaller than 123456789
*  (see also Wolfram Alpha).On the other hand, there are only 511 distinct
*  positive integers having their digits arranged in ascending order.
*  Therefore, it is better to start with numbers that have properly arranged
*  digits and then check if they are prime numbers.The method of generating
*  a sequence of such numbers is not indifferent.We want this sequence to be
*  monotonically increasing, because then additional sorting of results will
*  be unnecessary. It turns out that by using a queue we can easily get the
*  desired effect. Additionally, the algorithm then does not use recursion
*  (although the program probably does not have to comply with the MISRA
*  standard). The problem to be solved is the queue size, the a priori
*  assumption that 1000 is good enough, but a bit magical.
*/

package example.rossetacode.ascendingprimes;

import java.util.Arrays;

public class Program implements Runnable {

public static void main(String[] args) {
long t1 = System.nanoTime();
new Program().run();
long t2 = System.nanoTime();
System.out.println(
"total time consumed = " + (t2 - t1) * 1E-6 + " milliseconds");
}

public void run() {

final int MAX_SIZE = 1000;
final int[] queue = new int[MAX_SIZE];
int begin = 0;
int end = 0;

for (int k = 1; k <= 9; k++) {
queue[end++] = k;
}

while (begin < end) {
int n = queue[begin++];
for (int k = n % 10 + 1; k <= 9; k++) {
queue[end++] = n * 10 + k;
}
}

// We can use a parallel stream (and then sort the results)
// to use multiple cores.
//
System.out.println(Arrays.stream(queue).filter(this::isPrime).boxed().toList());
}

private boolean isPrime(int n) {
if (n == 2) {
return true;
}
if (n == 1 || n % 2 == 0) {
return false;
}
int root = (int) Math.sqrt(n);
for (int k = 3; k <= root; k += 2) {
if (n % k == 0) {
return false;
}
}
return true;
}
}
```
Output:
```[2, 3, 5, 7, 13, 17, 19, 23, 29, 37, 47, 59, 67, 79, 89, 127, 137, 139, 149, 157, 167, 179, 239, 257, 269, 347, 349, 359, 367, 379, 389, 457, 467, 479, 569, 1237, 1249, 1259, 1279, 1289, 1367, 1459, 1489, 1567, 1579, 1789, 2347, 2357, 2389, 2459, 2467, 2579, 2689, 2789, 3457, 3467, 3469, 4567, 4679, 4789, 5689, 12347, 12379, 12457, 12479, 12569, 12589, 12689, 13457, 13469, 13567, 13679, 13789, 15679, 23459, 23567, 23689, 23789, 25679, 34589, 34679, 123457, 123479, 124567, 124679, 125789, 134789, 145679, 234589, 235679, 235789, 245789, 345679, 345689, 1234789, 1235789, 1245689, 1456789, 12356789, 23456789]
total time consumed = 4.964799999999999 milliseconds```

## JavaScript

Translation of: Java
```<!DOCTYPE html>
<html>
<body>
<noscript>
No script, no fun. Turn on Javascript on.
</noscript>

<script>
(()=>{

function isPrime(n) {
if (n == 2)
return true;
if (n == 1 || n % 2 == 0)
return false;
root = Math.sqrt(n)
for (let k = 3; k <= root; k += 2)
if (n % k == 0)
return false;
return true;
}

let queue = [];
let primes = [];

for (let k = 1; k <= 9; k++)
queue.push(k);

while (queue.length != 0)
{
let n = queue.shift();
if (isPrime(n))
primes.push(n);
for (let k = n % 10 + 1; k <= 9; k++)
queue.push(n * 10 + k);
}

document.writeln(primes);

})();
</script>

</body>
</html>
```
Output:
`2,3,5,7,13,17,19,23,29,37,47,59,67,79,89,127,137,139,149,157,167,179,239,257,269,347,349,359,367,379,389,457,467,479,569,1237,1249,1259,1279,1289,1367,1459,1489,1567,1579,1789,2347,2357,2389,2459,2467,2579,2689,2789,3457,3467,3469,4567,4679,4789,5689,12347,12379,12457,12479,12569,12589,12689,13457,13469,13567,13679,13789,15679,23459,23567,23689,23789,25679,34589,34679,123457,123479,124567,124679,125789,134789,145679,234589,235679,235789,245789,345679,345689,1234789,1235789,1245689,1456789,12356789,23456789`

## jq

Works with: jq

Works with gojq, the Go implementation of jq

See Erdős-primes#jq for a suitable definition of `is_prime` as used here.

```# Output: the stream of ascending primes, in order
def ascendingPrimes:
# Generate the stream of primes beginning with the digit .
# and with strictly ascending digits, without regard to order
def generate:
# strings
def g:
. as \$first
| tonumber as \$n
| select(\$n <= 9)
| \$first,
((range(\$n + 1;10) | tostring | g) as \$x
| \$first + \$x );
tostring | g | tonumber | select(is_prime);

[range(1;10) | generate] | sort[];

def lpad(\$len): tostring | (\$len - length) as \$l | (" " * \$l)[:\$l] + .;
[ascendingPrimes]
| "There are \(length) ascending primes, namely:",
( _nwise(10) | map(lpad(10)) | join(" ") );

Output:
```There are 100 ascending primes, namely:
2          3          5          7         13         17         19         23         29         37
47         59         67         79         89        127        137        139        149        157
167        179        239        257        269        347        349        359        367        379
389        457        467        479        569       1237       1249       1259       1279       1289
1367       1459       1489       1567       1579       1789       2347       2357       2389       2459
2467       2579       2689       2789       3457       3467       3469       4567       4679       4789
5689      12347      12379      12457      12479      12569      12589      12689      13457      13469
13567      13679      13789      15679      23459      23567      23689      23789      25679      34589
34679     123457     123479     124567     124679     125789     134789     145679     234589     235679
235789     245789     345679     345689    1234789    1235789    1245689    1456789   12356789   23456789
```

## Julia

```using Combinatorics
using Primes

function ascendingprimes()
return filter(isprime, [evalpoly(10, reverse(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(ascendingprimes()))

@time ascendingprimes()
```
Output:
```2         3         5         7         13        17        19        23        29        37
47        59        67        79        89        127       137       139       149       157
167       179       239       257       269       347       349       359       367       379
389       457       467       479       569       1237      1249      1259      1279      1289
1367      1459      1489      1567      1579      1789      2347      2357      2389      2459
2467      2579      2689      2789      3457      3467      3469      4567      4679      4789
5689      12347     12379     12457     12479     12569     12589     12689     13457     13469
13567     13679     13789     15679     23459     23567     23689     23789     25679     34589
34679     123457    123479    124567    124679    125789    134789    145679    234589    235679
235789    245789    345679    345689    1234789   1235789   1245689   1456789   12356789  23456789

0.000150 seconds (2.19 k allocations: 159.078 KiB
```

## Lua

Exactly 511 calls to `is_prime` required.

```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 ascending_primes()
local digits, candidates, primes = {1,2,3,4,5,6,7,8,9}, {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(ascending_primes(), ", "))
```
Output:
`2, 3, 5, 7, 13, 17, 19, 23, 29, 37, 47, 59, 67, 79, 89, 127, 137, 139, 149, 157, 167, 179, 239, 257, 269, 347, 349, 359, 367, 379, 389, 457, 467, 479, 569, 1237, 1249, 1259, 1279, 1289, 1367, 1459, 1489, 1567, 1579, 1789, 2347, 2357, 2389, 2459, 2467, 2579, 2689, 2789, 3457, 3467, 3469, 4567, 4679, 4789, 5689, 12347, 12379, 12457, 12479, 12569, 12589, 12689, 13457, 13469, 13567, 13679, 13789, 15679, 23459, 23567, 23689, 23789, 25679, 34589, 34679, 123457, 123479, 124567, 124679, 125789, 134789, 145679, 234589, 235679, 235789, 245789, 345679, 345689, 1234789, 1235789, 1245689, 1456789, 12356789, 23456789`

## Matlab

Translation of: Java
```queue = 1:9;

j = 1;
while j < length(queue)
n = queue(j);
j = j + 1;
a = n * 10 + mod(n, 10) + 1;
b = n * 10 + 9;
if a <= b
queue = [queue, a:b];
end
end

queue(isprime(queue))
```
Output:
```ans =

Columns 1 through 8

2           3           5           7          13          17          19          23

Columns 9 through 16

29          37          47          59          67          79          89         127

Columns 17 through 24

137         139         149         157         167         179         239         257

Columns 25 through 32

269         347         349         359         367         379         389         457

Columns 33 through 40

467         479         569        1237        1249        1259        1279        1289

Columns 41 through 48

1367        1459        1489        1567        1579        1789        2347        2357

Columns 49 through 56

2389        2459        2467        2579        2689        2789        3457        3467

Columns 57 through 64

3469        4567        4679        4789        5689       12347       12379       12457

Columns 65 through 72

12479       12569       12589       12689       13457       13469       13567       13679

Columns 73 through 80

13789       15679       23459       23567       23689       23789       25679       34589

Columns 81 through 88

34679      123457      123479      124567      124679      125789      134789      145679

Columns 89 through 96

234589      235679      235789      245789      345679      345689     1234789     1235789

Columns 97 through 100

1245689     1456789    12356789    23456789```

## Mathematica/Wolfram Language

```ps=Sort@Select[FromDigits /@ Subsets[Range@9, {1, \[Infinity]}], PrimeQ];
Multicolumn[ps, {Automatic, 6}, Appearance -> "Horizontal"]
```
Output:
```2	3	5	7	13	17	19	23
29	37	47	59	67	79	89	127
137	139	149	157	167	179	239	257
269	347	349	359	367	379	389	457
467	479	569	1237	1249	1259	1279	1289
1367	1459	1489	1567	1579	1789	2347	2357
2389	2459	2467	2579	2689	2789	3457	3467
3469	4567	4679	4789	5689	12347	12379	12457
12479	12569	12589	12689	13457	13469	13567	13679
13789	15679	23459	23567	23689	23789	25679	34589
34679	123457	123479	124567	124679	125789	134789	145679
234589	235679	235789	245789	345679	345689	1234789	1235789
1245689	1456789	12356789	23456789```

## Nim

We build the candidates using a loop by increasing length. Our solution needs only 502 primality tests.

```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 ascendingPrimes(): 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 (item.lastDigit + 1)..9:
let newVal = 10 * item.val + newDigit
if newVal.isPrime():
yield newVal
items = move(nextItems)

var rank = 0
for prime in ascendingPrimes():
inc rank
stdout.write (\$prime).align(8)
stdout.write if rank mod 10 == 0: '\n' else: ' '
```
Output:
```       2        3        5        7       13       17       19       23       29       37
47       59       67       79       89      127      137      139      149      157
167      179      239      257      269      347      349      359      367      379
389      457      467      479      569     1237     1249     1259     1279     1289
1367     1459     1489     1567     1579     1789     2347     2357     2389     2459
2467     2579     2689     2789     3457     3467     3469     4567     4679     4789
5689    12347    12379    12457    12479    12569    12589    12689    13457    13469
13567    13679    13789    15679    23459    23567    23689    23789    25679    34589
34679   123457   123479   124567   124679   125789   134789   145679   234589   235679
235789   245789   345679   345689  1234789  1235789  1245689  1456789 12356789 23456789
```

## OCaml

```let is_prime n =
let rec test x =
let q = n / x in x > q || x * q <> n && n mod (x + 2) <> 0 && test (x + 6)
in if n < 5 then n lor 1 = 3 else n land 1 <> 0 && n mod 3 <> 0 && test 5

let ascending_ints =
let rec range10 m d = if d < 10 then m + d :: range10 m (succ d) else [] in
let up n = range10 (n * 10) (succ (n mod 10)) in
let rec next l = if l = [] then [] else l @ next (List.concat_map up l) in
next [0]

let () =
List.filter is_prime ascending_ints
|> List.iter (Printf.printf " %u") |> print_newline
```
Output:
` 2 3 5 7 13 17 19 23 29 37 47 59 67 79 89 127 137 139 149 157 167 179 239 257 269 347 349 359 367 379 389 457 467 479 569 1237 1249 1259 1279 1289 1367 1459 1489 1567 1579 1789 2347 2357 2389 2459 2467 2579 2689 2789 3457 3467 3469 4567 4679 4789 5689 12347 12379 12457 12479 12569 12589 12689 13457 13469 13567 13679 13789 15679 23459 23567 23689 23789 25679 34589 34679 123457 123479 124567 124679 125789 134789 145679 234589 235679 235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789`

## Pascal

Translation of: JavaScript
```{\$mode Delphi}

{ Note that for the program to work properly,
integer variables must be at least 28-bit.
Free Pascal Compiler uses 16-bit integers by default,
so a directive like above is needed. }

program ascendingprimes(output);

const maxsize = 1000;

var
queue, primes : array[1..maxsize] of integer;
b, e, n, k, v : integer;

function isprime(n: integer): boolean;

var
ans : boolean;
root, k : integer;
begin
if n = 2 then
ans := true
else if (n = 1) or (n mod 2 = 0) then
ans := false
else
begin
root := trunc(sqrt(n));
ans := true;
k := 3;
while ans and (k <= root) do
if n mod k = 0 then
ans := false
else
k := k + 2;
end;
isprime := ans
end;

begin

b := 1;
e := 1;
n := 0;

for k := 1 to 9 do
begin
queue[e] := k;
e := e + 1
end;

while b < e do
begin
v := queue[b];
b := b + 1;
if isprime(v) then
begin
n := n + 1;
primes[n] := v
end;

for k := v mod 10 + 1 to 9 do
begin
queue[e] := v * 10 + k;
e := e + 1
end

end;

for k := 1 to n do
write(primes[k], ' ');
writeln()

end.
```
Output:
`2 3 5 7 13 17 19 23 29 37 47 59 67 79 89 127 137 139 149 157 167 179 239 257 269 347 349 359 367 379 389 457 467 479 569 1237 1249 1259 1279 1289 1367 1459 1489 1567 1579 1789 2347 2357 2389 2459 2467 2579 2689 2789 3457 3467 3469 4567 4679 4789 5689 12347 12379 12457 12479 12569 12589 12689 13457 13469 13567 13679 13789 15679 23459 23567 23689 23789 25679 34589 34679 123457 123479 124567 124679 125789 134789 145679 234589 235679 235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789 `

## Perl

Library: ntheory
```use strict;
use warnings;
use ntheory 'is_prime';

print join( '',
map { sprintf '%10d', \$_ }
sort { \$a <=> \$b }
grep /./ && is_prime \$_,
glob join '', map "{\$_,}", 1..9
) =~ s/.{50}\K/\n/gr;
```
Output:
```         2         3         5         7        13
17        19        23        29        37
47        59        67        79        89
127       137       139       149       157
167       179       239       257       269
347       349       359       367       379
389       457       467       479       569
1237      1249      1259      1279      1289
1367      1459      1489      1567      1579
1789      2347      2357      2389      2459
2467      2579      2689      2789      3457
3467      3469      4567      4679      4789
5689     12347     12379     12457     12479
12569     12589     12689     13457     13469
13567     13679     13789     15679     23459
23567     23689     23789     25679     34589
34679    123457    123479    124567    124679
125789    134789    145679    234589    235679
235789    245789    345679    345689   1234789
1235789   1245689   1456789  12356789  23456789
```

## Phix

```with javascript_semantics
function ascending_primes(sequence res, atom p=0)
for d=remainder(p,10)+1 to 9 do
integer np = p*10+d
if odd(d) and is_prime(np) then res &= np end if
res = ascending_primes(res,np)
end for
return res
end function

sequence r = apply(true,sprintf,{{"%8d"},sort(ascending_primes({2}))})
printf(1,"There are %,d ascending primes:\n%s\n",{length(r),join_by(r,1,10," ")})
```
Output:
```There are 100 ascending primes:
2        3        5        7       13       17       19       23       29       37
47       59       67       79       89      127      137      139      149      157
167      179      239      257      269      347      349      359      367      379
389      457      467      479      569     1237     1249     1259     1279     1289
1367     1459     1489     1567     1579     1789     2347     2357     2389     2459
2467     2579     2689     2789     3457     3467     3469     4567     4679     4789
5689    12347    12379    12457    12479    12569    12589    12689    13457    13469
13567    13679    13789    15679    23459    23567    23689    23789    25679    34589
34679   123457   123479   124567   124679   125789   134789   145679   234589   235679
235789   245789   345679   345689  1234789  1235789  1245689  1456789 12356789 23456789
```

### powerset

Using a powerset, the basic idea of which was taken from the Factor entry above, here incrementally built, does not need either recursion or a sort, same output

```with javascript_semantics
function ascending_primes()
sequence res = {}, powerset = {0}
while length(powerset) do
sequence next = {}
for i=1 to length(powerset) do
for d=remainder(powerset[i],10)+1 to 9 do
next &= powerset[i]*10+d
end for
end for
powerset = next
res &= filter(powerset,is_prime)
end while
return res
end function

sequence r = apply(true,sprintf,{{"%8d"},ascending_primes()})
printf(1,"There are %,d ascending primes:\n%s\n",{length(r),join_by(r,1,10," ")})
```

By way of explanation, specifically "no sort rqd", if you `pp(shorten(powerset,"entries",3))` at the end of each iteration then you get:

```{1,2,3, `...`, 7,8,9, ` (9 entries)`}
{12,13,14, `...`, 78,79,89, ` (36 entries)`}
{123,124,125, `...`, 679,689,789, ` (84 entries)`}
{1234,1235,1236, `...`, 5689,5789,6789, ` (126 entries)`}
{12345,12346,12347, `...`, 45789,46789,56789, ` (126 entries)`}
{123456,123457,123458, `...`, 346789,356789,456789, ` (84 entries)`}
{1234567,1234568,1234569, `...`, 2356789,2456789,3456789, ` (36 entries)`}
{12345678,12345679,12345689, `...`, 12456789,13456789,23456789, ` (9 entries)`}
{123456789}
{}
```

## PHP

Translation of: JavaScript
```<?php

function isPrime(\$n)
{
if (\$n == 2)
return true;
if (\$n == 1 || \$n % 2 == 0)
return false;
\$root = intval(sqrt(\$n));
for (\$k = 3; \$k <= \$root; \$k += 2)
if (\$n % \$k == 0)
return false;
return true;
}

\$queue = [];
\$primes = [];

\$begin = 0;
\$end = 0;

for (\$k = 1; \$k <= 9; \$k++)
\$queue[\$end++] = \$k;

while (\$begin < \$end)
{
\$n = \$queue[\$begin++];

if (isPrime(\$n))
\$primes[] = \$n;
for (\$k = \$n % 10 + 1; \$k <= 9; \$k++)
\$queue[\$end++] = \$n * 10 + \$k;
}

foreach(\$primes as \$p)
echo "\$p ";
```
Output:
`2 3 5 7 13 17 19 23 29 37 47 59 67 79 89 127 137 139 149 157 167 179 239 257 269 347 349 359 367 379 389 457 467 479 569 1237 1249 1259 1279 1289 1367 1459 1489 1567 1579 1789 2347 2357 2389 2459 2467 2579 2689 2789 3457 3467 3469 4567 4679 4789 5689 12347 12379 12457 12479 12569 12589 12689 13457 13469 13567 13679 13789 15679 23459 23567 23689 23789 25679 34589 34679 123457 123479 124567 124679 125789 134789 145679 234589 235679 235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789 `

## Picat

```import util.

main =>
DP = [N : S in power_set("123456789"), 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)```
Output:
```        2        3        5        7       13       17       19       23       29       37
47       59       67       79       89      127      137      139      149      157
167      179      239      257      269      347      349      359      367      379
389      457      467      479      569     1237     1249     1259     1279     1289
1367     1459     1489     1567     1579     1789     2347     2357     2389     2459
2467     2579     2689     2789     3457     3467     3469     4567     4679     4789
5689    12347    12379    12457    12479    12569    12589    12689    13457    13469
13567    13679    13789    15679    23459    23567    23689    23789    25679    34589
34679   123457   123479   124567   124679   125789   134789   145679   234589   235679
235789   245789   345679   345689  1234789  1235789  1245689  1456789 12356789 23456789

len = 100```

## PicoLisp

```(de prime? (N)
(or
(= N 2)
(and
(> N 1)
(bit? 1 N)
(for (D 3  T  (+ D 2))
(T (> D (sqrt N)) T)
(T (=0 (% N D)) NIL) ) ) ) )
(let
(D 2
L (1 2 2 . (4 2 4 2 4 6 2 6 .))
Lst
(make
(while (>= 23456789 D)
(and
(prime? D)
(apply < (chop D))
(inc 'D (++ L)) ) ) )
(let Fmt (need 10 10)
(while (cut 10 'Lst)
(apply tab @ Fmt) ) ) )```
Output:
```         2         3         5         7        13        17        19        23        29        37
47        59        67        79        89       127       137       139       149       157
167       179       239       257       269       347       349       359       367       379
389       457       467       479       569      1237      1249      1259      1279      1289
1367      1459      1489      1567      1579      1789      2347      2357      2389      2459
2467      2579      2689      2789      3457      3467      3469      4567      4679      4789
5689     12347     12379     12457     12479     12569     12589     12689     13457     13469
13567     13679     13789     15679     23459     23567     23689     23789     25679     34589
34679    123457    123479    124567    124679    125789    134789    145679    234589    235679
235789    245789    345679    345689   1234789   1235789   1245689   1456789  12356789  23456789
```

## Prolog

Works with: swi-prolog
```isPrime(2).
isPrime(N):-
between(3, inf, N),
N /\ 1 > 0,             % odd
M is floor(sqrt(N)) - 1, % reverse 2*I+1
Max is M div 2,
forall(between(1, Max, I), N mod (2*I+1) > 0).

combi(0, _, Num, Num).
combi(N, [X|T], Acc, Num):-
N > 0,
N1 is N - 1,
Acc1 is Acc * 10 + X,
combi(N1, T, Acc1, Num).
combi(N, [_|T], Acc, Num):-
N > 0,
combi(N, T, Acc, Num).

ascPrimes(Num):-
between(1, 9, N),
combi(N, [1, 2, 3, 4, 5, 6, 7, 8, 9], 0, Num),
isPrime(Num).

showList(List):-
findnsols(10, DPrim, (member(DPrim, List), writef('%9r', [DPrim])), _),
nl,
fail.
showList(_).

do:-findall(DPrim, ascPrimes(DPrim), DList),
showList(DList).
```
Output:
```?- do.
2        3        5        7       13       17       19       23       29       37
47       59       67       79       89      127      137      139      149      157
167      179      239      257      269      347      349      359      367      379
389      457      467      479      569     1237     1249     1259     1279     1289
1367     1459     1489     1567     1579     1789     2347     2357     2389     2459
2467     2579     2689     2789     3457     3467     3469     4567     4679     4789
5689    12347    12379    12457    12479    12569    12589    12689    13457    13469
13567    13679    13789    15679    23459    23567    23689    23789    25679    34589
34679   123457   123479   124567   124679   125789   134789   145679   234589   235679
235789   245789   345679   345689  1234789  1235789  1245689  1456789 12356789 23456789
true.
```

## Python

### Recursive solution, with a number generator and sorting of results.

```from sympy import isprime

def ascending(x=0):
for y in range(x*10 + (x%10) + 1, x*10 + 10):
yield from ascending(y)
yield(y)

print(sorted(x for x in ascending() if isprime(x)))
```
Output:
`[2, 3, 5, 7, 13, 17, 19, 23, 29, 37, 47, 59, 67, 79, 89, 127, 137, 139, 149, 157, 167, 179, 239, 257, 269, 347, 349, 359, 367, 379, 389, 457, 467, 479, 569, 1237, 1249, 1259, 1279, 1289, 1367, 1459, 1489, 1567, 1579, 1789, 2347, 2357, 2389, 2459, 2467, 2579, 2689, 2789, 3457, 3467, 3469, 4567, 4679, 4789, 5689, 12347, 12379, 12457, 12479, 12569, 12589, 12689, 13457, 13469, 13567, 13679, 13789, 15679, 23459, 23567, 23689, 23789, 25679, 34589, 34679, 123457, 123479, 124567, 124679, 125789, 134789, 145679, 234589, 235679, 235789, 245789, 345679, 345689, 1234789, 1235789, 1245689, 1456789, 12356789, 23456789]`

### Queue-based solution that does not need sorting.

Translation of: Pascal
```def isprime(n):
if n == 2: return True
if n == 1 or n % 2 == 0: return False
root1 = int(n**0.5) + 1;
for k in range(3, root1, 2):
if n % k == 0: return False
return True

queue = [k for k in range(1, 10)]
primes = []

while queue:
n = queue.pop(0)
if isprime(n):
primes.append(n)
queue.extend(n * 10 + k for k in range(n % 10 + 1, 10))

print(primes)
```
Output:
`[2, 3, 5, 7, 13, 17, 19, 23, 29, 37, 47, 59, 67, 79, 89, 127, 137, 139, 149, 157, 167, 179, 239, 257, 269, 347, 349, 359, 367, 379, 389, 457, 467, 479, 569, 1237, 1249, 1259, 1279, 1289, 1367, 1459, 1489, 1567, 1579, 1789, 2347, 2357, 2389, 2459, 2467, 2579, 2689, 2789, 3457, 3467, 3469, 4567, 4679, 4789, 5689, 12347, 12379, 12457, 12479, 12569, 12589, 12689, 13457, 13469, 13567, 13679, 13789, 15679, 23459, 23567, 23689, 23789, 25679, 34589, 34679, 123457, 123479, 124567, 124679, 125789, 134789, 145679, 234589, 235679, 235789, 245789, 345679, 345689, 1234789, 1235789, 1245689, 1456789, 12356789, 23456789]`

## Quackery

`powerset` is defined at Power set#Quackery, and `isprime` is defined at Primality by trial division#Quackery.

```  [ 0 swap witheach
[ swap 10 * + ] ]                 is digits->n ( [ --> n )

[]
' [ 1 2 3 4 5 6 7 8 9 ] powerset
witheach
[ digits->n dup isprime
iff join else drop ]
sort echo```
Output:
```[ 2 3 5 7 13 17 19 23 29 37 47 59 67 79 89 127 137 139 149 157 167 179 239 257 269 347 349 359 367 379 389 457 467 479 569 1237 1249 1259 1279 1289 1367 1459 1489 1567 1579 1789 2347 2357 2389 2459 2467 2579 2689 2789 3457 3467 3469 4567 4679 4789 5689 12347 12379 12457 12479 12569 12589 12689 13457 13469 13567 13679 13789 15679 23459 23567 23689 23789 25679 34589 34679 123457 123479 124567 124679 125789 134789 145679 234589 235679 235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789 ]
```

## Raku

```put (flat 2, 3, 5, 7, sort +*, gather (1..8).map: &recurse ).batch(10)».fmt("%8d").join: "\n";

sub recurse (\$str) {
.take for (\$str X~ (3, 7, 9)).grep: { .is-prime && [<] .comb };
recurse \$str × 10 + \$_ for \$str % 10 ^.. 9;
}

printf "%.3f seconds", now - INIT now;
```
Output:
```       2        3        5        7       13       17       19       23       29       37
47       59       67       79       89      127      137      139      149      157
167      179      239      257      269      347      349      359      367      379
389      457      467      479      569     1237     1249     1259     1279     1289
1367     1459     1489     1567     1579     1789     2347     2357     2389     2459
2467     2579     2689     2789     3457     3467     3469     4567     4679     4789
5689    12347    12379    12457    12479    12569    12589    12689    13457    13469
13567    13679    13789    15679    23459    23567    23689    23789    25679    34589
34679   123457   123479   124567   124679   125789   134789   145679   234589   235679
235789   245789   345679   345689  1234789  1235789  1245689  1456789 12356789 23456789
0.075 seconds```

## Ring

```show("ascending primes", sort(cending_primes(seq(1, 9))))

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
next
next
return pr

func fmt(x, l)
res = "          " + x
return right(res, l)```
Output:
```100 ascending primes:
2        3        5        7       13
17       19       23       29       37
47       59       67       79       89
127      137      139      149      157
167      179      239      257      269
347      349      359      367      379
389      457      467      479      569
1237     1249     1259     1279     1289
1367     1459     1489     1567     1579
1789     2347     2357     2389     2459
2467     2579     2689     2789     3457
3467     3469     4567     4679     4789
5689    12347    12379    12457    12479
12569    12589    12689    13457    13469
13567    13679    13789    15679    23459
23567    23689    23789    25679    34589
34679   123457   123479   124567   124679
125789   134789   145679   234589   235679
235789   245789   345679   345689  1234789
1235789  1245689  1456789 12356789 23456789```

## RPL

Thanks to recursion, we have here a compact and efficient code that generates only ascending odd integers with 9 digits and less, and then check their primality.

Works with: Halcyon Calc version 4.2.7
RPL code Comment
``` ≪ IF DUP 5 ≤ THEN { 2 3 5 } SWAP POS
ELSE
IF DUP 2 MOD NOT THEN 2
ELSE
DUP √ CEIL → lim
≪ 3 WHILE DUP2 MOD OVER lim ≤ AND REPEAT 2 + END
≫
END MOD
END SIGN
≫ 'PRIM?' STO

≪
SWAP 1 - SWAP
10 * LAST MOD 1 +
IF 3 PICK NOT THEN DUP 2 MOD NOT + END
+ LAST DROP 9 4 PICK - + FOR d
IF DUP
THEN SWAP OVER d APRIM SWAP
ELSE
IF d PRIM? THEN SWAP d + SWAP END
d 1 + 'd' STO
END
NEXT DROP
≫ 'APRIM' STO
```
```PRIM? ( n -- boolean)

APRIM ( { } n seed -- { asc } )
n ← n-1
preparing loop from ##u to ##v, where ## = seed,
u = last digit of seed + 1 (or + 2 if last recursion
and seed odd) ;  v = 10 - n
if not last recursion
generate next digits
else
store in list if prime
.
forget n
.
```
Input:
```≪ { 2 } 1 9 FOR n n 0 APRIM NEXT ≫ EVAL
```
Output:
```1: { 2 3 5 7 13 17 19 23 29 37 47 59 67 79 89 127 137 139 149 157 167 179 239 257 269 347 349 359 367 379 389 457 467 479 569 1237 1249 1259 1279 1289 1367 1459 1489 1567 1579 1789 2347 2357 2389 2459 2467 2579 2689 2789 3457 3467 3469 4567 4679 4789 5689 12347 12379 12457 12479 12569 12589 12689 13457 13469 13567 13679 13789 15679 23459 23567 23689 23789 25679 34589 34679 123457 123479 124567 124679 125789 134789 145679 234589 235679 235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789 }
```

## Ruby

```require 'prime'

digits = [9,8,7,6,5,4,3,2,1]
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(",")
```
Output:
```2,3,5,7,13,17,19,23,29,37,47,59,67,79,89,127,137,139,149,157,167,179,239,257,269,347,349,359,367,379,389,457,467,479,569,1237,1249,1259,1279,1289,1367,1459,1489,1567,1579,1789,2347,2357,2389,2459,2467,2579,2689,2789,3457,3467,3469,4567,4679,4789,5689,12347,12379,12457,12479,12569,12589,12689,13457,13469,13567,13679,13789,15679,23459,23567,23689,23789,25679,34589,34679,123457,123479,124567,124679,125789,134789,145679,234589,235679,235789,245789,345679,345689,1234789,1235789,1245689,1456789,12356789,23456789
```

## Sidef

```func primes_with_ascending_digits(base = 10) {

var list = []
var digits = @(1..^base -> flip)

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 arr = primes_with_ascending_digits()

say "There are #{arr.len} ascending primes.\n"

arr.each_slice(10, {|*a|
say a.map { '%8s' % _ }.join(' ')
})
```
Output:
```There are 100 ascending primes.

2        3        5        7       13       17       19       23       29       37
47       59       67       79       89      127      137      139      149      157
167      179      239      257      269      347      349      359      367      379
389      457      467      479      569     1237     1249     1259     1279     1289
1367     1459     1489     1567     1579     1789     2347     2357     2389     2459
2467     2579     2689     2789     3457     3467     3469     4567     4679     4789
5689    12347    12379    12457    12479    12569    12589    12689    13457    13469
13567    13679    13789    15679    23459    23567    23689    23789    25679    34589
34679   123457   123479   124567   124679   125789   134789   145679   234589   235679
235789   245789   345679   345689  1234789  1235789  1245689  1456789 12356789 23456789
```

## SparForte

Translation of: Pascal
```#!/usr/local/bin/spar

pragma annotate( summary, "primes_asc" );
pragma annotate( description, "Generate and show all primes with strictly ascending decimal digits" );
pragma annotate( description, "Translation of Pascal" );
pragma annotate( see_also, "https://rosettacode.org/wiki/Ascending_primes" );
pragma annotate( author, "Ken O. Burtch" );

pragma software_model( nonstandard );
pragma restriction( no_external_commands );

procedure primes_asc is
maxsize : constant natural := 1000;

queue : array(1..maxsize) of natural;
primes: array(1..maxsize) of natural;

b : natural;
e : natural;
n : natural;
v : natural;

function is_prime(num: integer) return boolean is
found : boolean;
num_root : natural;
k : natural;
begin
if num = 2 then
found;
elsif (num = 1) or (num mod 2 = 0) then
found := false;
else
num_root := numerics.truncation(numerics.sqrt(num));
found;
k := 3;
while found and (k <= num_root) loop
if num mod k = 0 then
found := false;
else
k := @ + 2;
end if;
end loop;
end if;
return found;
end is_prime;

begin
b := 1;
e := 1;
n := 0;

for k in 1..9 loop
queue(e) := k;
e := e + 1;
end loop;

while b < e loop
v := queue(b);
b := @ + 1;
if is_prime(v) then
n := @ + 1;
primes(n) := v;
end if;

for k in v mod 10 + 1..9 loop
queue(e) := v * 10 + k;
e := @ + 1;
end loop;
end loop;

for k in 1..n loop
put(primes(k), "ZZZZZZZZ9");
if k mod 8 = 0 then
new_line;
end if;
end loop;
new_line;
end primes_asc;
```
Output:
```        2        3        5        7       13       17       19       23
29       37       47       59       67       79       89      127
137      139      149      157      167      179      239      257
269      347      349      359      367      379      389      457
467      479      569     1237     1249     1259     1279     1289
1367     1459     1489     1567     1579     1789     2347     2357
2389     2459     2467     2579     2689     2789     3457     3467
3469     4567     4679     4789     5689    12347    12379    12457
12479    12569    12589    12689    13457    13469    13567    13679
13789    15679    23459    23567    23689    23789    25679    34589
34679   123457   123479   124567   124679   125789   134789   145679
234589   235679   235789   245789   345679   345689  1234789  1235789
1245689  1456789 12356789 23456789
```

## Visual Basic .NET

```Module AscendingPrimes

Function isPrime(n As Integer)
n = Math.Abs(n)
If n = 2 Then
Return True
End If
If n = 1 Or n Mod 2 = 0 Then
Return False
End If
Dim root As Integer = Math.Sqrt(n)
For k = 3 To root Step 2
If n Mod k = 0 Then
Return False
End If
Next
Return True
End Function

Sub Main()

Dim queue As Queue(Of Integer) = New Queue(Of Integer)
Dim primes As List(Of Integer) = New List(Of Integer)

For k = 1 To 9
queue.Enqueue(k)
Next

While queue.Count > 0
Dim n As Integer = queue.Dequeue()
If (isPrime(n)) Then
End If
For k = n Mod 10 + 1 To 9
queue.Enqueue(n * 10 + k)
Next
End While

For Each p As Integer In primes
Console.Write(p)
Console.Write(" ")
Next
Console.WriteLine()

End Sub

End Module
```
Output:
`2 3 5 7 13 17 19 23 29 37 47 59 67 79 89 127 137 139 149 157 167 179 239 257 269 347 349 359 367 379 389 457 467 479 569 1237 1249 1259 1279 1289 1367 1459 1489 1567 1579 1789 2347 2357 2389 2459 2467 2579 2689 2789 3457 3467 3469 4567 4679 4789 5689 12347 12379 12457 12479 12569 12589 12689 13457 13469 13567 13679 13789 15679 23459 23567 23689 23789 25679 34589 34679 123457 123479 124567 124679 125789 134789 145679 234589 235679 235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789`

## V (Vlang)

Translation of: Go
```fn is_prime(n int) bool {
if n < 2 {
return false
} else if n%2 == 0 {
return n == 2
} else if n%3 == 0 {
return n == 3
} else {
mut d := 5
for d*d <= n {
if n%d == 0 {
return false
}
d += 2
if n%d == 0 {
return false
}
d += 4
}
return true
}
}
fn generate(first int, cand int, digits int, mut asc map[int]bool) {
if digits == 0 {
if is_prime(cand) {
asc[cand] = true
}
return
}
for i in first..10 {
next := cand*10 + i
generate(i+1, next, digits-1, mut asc)
}
}

fn main() {
mut asc_primes_set := map[int]bool{} // avoids duplicates

for digits in 1..10 {
generate(1, 0, digits, mut asc_primes_set)
}
le := asc_primes_set.keys().len
mut asc_primes := []int{len: le}
mut i := 0
for k,_ in asc_primes_set {
asc_primes[i] = k
i++
}
asc_primes.sort()
println("There are \$le ascending primes, namely:")
for q in 0..le {
print("\${asc_primes[q]:8} ")
if (q+1)%10 == 0 {
println('')
}
}
}```
Output:
```There are 100 ascending primes, namely:
2        3        5        7       13       17       19       23       29       37
47       59       67       79       89      127      137      139      149      157
167      179      239      257      269      347      349      359      367      379
389      457      467      479      569     1237     1249     1259     1279     1289
1367     1459     1489     1567     1579     1789     2347     2357     2389     2459
2467     2579     2689     2789     3457     3467     3469     4567     4679     4789
5689    12347    12379    12457    12479    12569    12589    12689    13457    13469
13567    13679    13789    15679    23459    23567    23689    23789    25679    34589
34679   123457   123479   124567   124679   125789   134789   145679   234589   235679
235789   245789   345679   345689  1234789  1235789  1245689  1456789 12356789 23456789
```

## Wren

Library: Wren-math
Library: Wren-seq
Library: Wren-fmt

### Version 1 (Sieve)

Although they use a lot of memory, sieves usually produce good results in Wren and here we only need to sieve for primes up to 3456789 as there are just 9 possible candidates with 8 digits and 1 possible candidate with 9 digits which we can test for primality individually. The following runs in around 0.43 seconds.

```import "./math" for Int
import "./fmt"  for Fmt

var isAscending = Fn.new { |n|
if (n < 10) return true
var digits = Int.digits(n)
for (i in 1...digits.count) {
if (digits[i] <= digits[i-1]) return false
}
return true
}

var higherPrimes = []
var candidates = [
12345678, 12345679, 12345689, 12345789, 12346789,
12356789, 12456789, 13456789, 23456789, 123456789
]
for (cand in candidates) if (Int.isPrime(cand)) higherPrimes.add(cand)

var primes = Int.primeSieve(3456789)
var ascPrimes = []
for (p in primes) if (isAscending.call(p)) ascPrimes.add(p)
System.print("There are %(ascPrimes.count) ascending primes, namely:")
Fmt.tprint("\$8d", ascPrimes, 10)
```
Output:
```There are 100 ascending primes, namely:
2        3        5        7       13       17       19       23       29       37
47       59       67       79       89      127      137      139      149      157
167      179      239      257      269      347      349      359      367      379
389      457      467      479      569     1237     1249     1259     1279     1289
1367     1459     1489     1567     1579     1789     2347     2357     2389     2459
2467     2579     2689     2789     3457     3467     3469     4567     4679     4789
5689    12347    12379    12457    12479    12569    12589    12689    13457    13469
13567    13679    13789    15679    23459    23567    23689    23789    25679    34589
34679   123457   123479   124567   124679   125789   134789   145679   234589   235679
235789   245789   345679   345689  1234789  1235789  1245689  1456789 12356789 23456789
```

### Version 2 (Generator)

Library: Wren-set

Here we generate all possible positive integers with ascending non-zero digits and filter out those that are prime.

Much quicker than the 'sieve' approach at 0.013 seconds. I also tried using a powerset but that was slightly slower at 0.015 seconds.

```import "./set" for Set
import "./math" for Int
import "./fmt" for Fmt

var ascPrimes = Set.new() // avoids duplicates

var generate  // recursive function
generate = Fn.new { |first, cand, digits|
if (digits == 0) {
return
}
var i = first
while (i <= 9) {
var next = cand * 10 + i
generate.call(i + 1, next, digits - 1)
i = i + 1
}
}

for (digits in 1..9) generate.call(1, 0, digits)
ascPrimes = ascPrimes.toList
ascPrimes.sort()
System.print("There are %(ascPrimes.count) ascending primes, namely:")
Fmt.tprint("\$8d", ascPrimes, 10)
```
Output:
```Same as before.
```

## XPL0

Brute force solution: 4.3 seconds on Pi4.

```func IsPrime(N);        \Return 'true' if N is prime
int  N, I;
[if N <= 2 then return N = 2;
if (N&1) = 0 then \even >2\ return false;
for I:= 3 to sqrt(N) do
[if rem(N/I) = 0 then return false;
I:= I+1;
];
return true;
];

func Ascending(N);      \Return 'true' if digits are ascending
int  N, D;
[N:= N/10;
D:= rem(0);
while N do
[N:= N/10;
if rem(0) >= D then return false;
D:= rem(0);
];
return true;
];

int Cnt, N;
[Cnt:= 0;
Format(9, 0);
for N:= 2 to 123_456_789 do
if Ascending(N) then
if IsPrime(N) then
[RlOut(0, float(N));
Cnt:= Cnt+1;
if rem(Cnt/10) = 0 then CrLf(0);
];
]```
Output:
```        2        3        5        7       13       17       19       23       29       37
47       59       67       79       89      127      137      139      149      157
167      179      239      257      269      347      349      359      367      379
389      457      467      479      569     1237     1249     1259     1279     1289
1367     1459     1489     1567     1579     1789     2347     2357     2389     2459
2467     2579     2689     2789     3457     3467     3469     4567     4679     4789
5689    12347    12379    12457    12479    12569    12589    12689    13457    13469
13567    13679    13789    15679    23459    23567    23689    23789    25679    34589
34679   123457   123479   124567   124679   125789   134789   145679   234589   235679
235789   245789   345679   345689  1234789  1235789  1245689  1456789 12356789 23456789
```

### powerset

Aaah! Power set, from Factor. Runs in less than 1 millisecond. A better way of measuring duration than using Linux's time utility gave a more credible 35 milliseconds.

```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:= 1;
N:= N*10 + Digit;
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);
];
];
]```
Output:
```Same as before.
```