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# Primes with digits in nondecreasing order

Primes with digits in nondecreasing order is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
Task

Find all primes   (n)   with their decimal digits in non-decreasing order,   where   n   <   1,000

## ALGOL 68

`BEGIN # find primes where the digits are non-descending #    INT max number = 1000;    # sieve the primes to max number #    PR read "primes.incl.a68" PR    []BOOL prime = PRIMESIEVE max number;    # we can easily generate candidate numbers with a few nested loops #    INT p count := 0;    # apart from 1 digit primes, the final digit can only be 1, 3, 7 or 9 #    # however we don't optimise that here                                 #    FOR h FROM 0 TO 9 DO        FOR i FROM h TO 9 DO            INT hi = ( h * 10 ) + i;            FOR j FROM i TO 9 DO                INT hij = ( 10 * hi ) + j;                FOR k FROM IF j = 0 THEN 1 ELSE j FI TO 9                WHILE INT hijk = ( hij * 10 ) + k;                      hijk <= max number                DO                    IF prime[ hijk ] THEN                        p count +:= 1;                        print( ( " ", whole( hijk, -6 ) ) );                        IF p count MOD 12 = 0 THEN print( ( newline ) ) FI                    FI                OD # k #            OD # j #        OD # i #    OD # h # ;    print( ( newline           , newline           , "Found "           , whole( p count, 0 )           , " non-descending primes up to "           , whole( max number, 0 )           , newline           )         )END`
Output:
```      2      3      5      7     11     13     17     19     23     29     37     47
59     67     79     89    113    127    137    139    149    157    167    179
199    223    227    229    233    239    257    269    277    337    347    349
359    367    379    389    449    457    467    479    499    557    569    577
599    677

Found 50 non-descending primes up to 1000
```

## APL

Works with: Dyalog APL
`(⊢(/⍨)(∧/2≤/10(⊥⍣¯1)⊢)¨)∘(⊢(/⍨)(2=0+.=⍳|⊢)¨)⍳1000`
Output:
```2 3 5 7 11 13 17 19 23 29 37 47 59 67 79 89 113 127 137 139 149 157 167
179 199 223 227 229 233 239 257 269 277 337 347 349 359 367 379
389 449 457 467 479 499 557 569 577 599 677```

## Arturo

`primes: select 1..1000 => prime?nondecreasing?: function [n][    ds: digits n    if 1 = size ds -> return true    lastDigit: first ds    loop 1..dec size ds 'i [        digit: ds\[i]        if digit < lastDigit -> return false        lastDigit: digit    ]     return true] loop split.every: 10 select primes => nondecreasing? 'a ->     print map a => [pad to :string & 4]`
Output:
```   2    3    5    7   11   13   17   19   23   29
37   47   59   67   79   89  113  127  137  139
149  157  167  179  199  223  227  229  233  239
257  269  277  337  347  349  359  367  379  389
449  457  467  479  499  557  569  577  599  677```

## AWK

` # syntax: GAWK -f PRIMES_WITH_DIGITS_IN_NONDECREASING_ORDER.AWKBEGIN {    start = 1    stop = 1000    for (i=start; i<=stop; i++) {      if (is_prime(i)) {        flag = 1        for (j=1; j<length(i); j++) {          if (substr(i,j,1) > substr(i,j+1,1)) {            flag = 0          }        }        if (flag == 1) {          printf("%4d%1s",i,++count%10?"":"\n")        }      }    }    printf("\nPrimes with digits in nondecreasing order %d-%d: %d\n",start,stop,count)    exit(0)}function is_prime(x,  i) {    if (x <= 1) {      return(0)    }    for (i=2; i<=int(sqrt(x)); i++) {      if (x % i == 0) {        return(0)      }    }    return(1)} `
Output:
```   2    3    5    7   11   13   17   19   23   29
37   47   59   67   79   89  113  127  137  139
149  157  167  179  199  223  227  229  233  239
257  269  277  337  347  349  359  367  379  389
449  457  467  479  499  557  569  577  599  677

Primes with digits in nondecreasing order 1-1000: 50
```

## BASIC

`10 DEFINT A-Z20 DIM P(1000)30 P(0)=-1: P(1)=-140 FOR I=2 TO SQR(1000)50 IF P(I)=0 THEN FOR J=I+I TO 1000 STEP I: P(J)=-1: NEXT60 NEXT70 FOR A=0 TO 9: FOR B=A TO 9: FOR C=B TO 980 N=A*100+B*10+C90 IF P(N)=0 THEN PRINT N,100 NEXT C,B,A`
Output:
``` 2             3             5             7             11
13            17            19            23            29
37            47            59            67            79
89            113           127           137           139
149           157           167           179           199
223           227           229           233           239
257           269           277           337           347
349           359           367           379           389
449           457           467           479           499
557           569           577           599           677```

## BCPL

`get "libhdr"; let sieve(prime, max) be\$(  0!prime := false    1!prime := false    for i=2 to max do i!prime := true    for i=2 to max/2        if i!prime        \$(  let j = i*2            while j <= max            \$(  j!prime := false                j := j + i            \$)        \$)\$) let start() be\$(  let prime = getvec(1000)    let c = 0    sieve(prime, 1000)     for d100 = 0 to 9        for d10 = d100 to 9            for d1 = d10 to 9            \$(  let n = d100*100 + d10*10 + d1                if n!prime then                \$(  writed(n,4)                    c := c + 1                    if c rem 10 = 0 then wrch('*N')                \$)            \$)    freevec(prime)\$)`
Output:
```   2   3   5   7  11  13  17  19  23  29
37  47  59  67  79  89 113 127 137 139
149 157 167 179 199 223 227 229 233 239
257 269 277 337 347 349 359 367 379 389
449 457 467 479 499 557 569 577 599 677```

## C#

The chars array explicitly enforces the case order, not relying on the language's idea of what letters are before or after each other.

`using System.Linq; using System.Collections.Generic; using static System.Console; using static System.Math; class Program {   static int ba; static string chars = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz";   // convert an int into a string using the current ba  static string from10(int b) { string res = ""; int re; while (b > 0) {    b = DivRem(b, ba, out re); res = chars[(byte)re] + res; } return res; }   // parse a string into an int, using current ba (not used here)  static int to10(string s) { int res = 0; foreach (char i in s)    res = res * ba + chars.IndexOf(i); return res; }   // note: comparing the index of the chars instead of the chars themsleves, which avoids case issues  static bool nd(string s) { if (s.Length < 2) return true;    char l = s[0]; for (int i = 1; i < s.Length; i++)      if (chars.IndexOf(l) > chars.IndexOf(s[i]))        return false; else l = s[i] ; return true; }   static void Main(string[] args) { int c, lim = 1000; string s;    foreach (var b in new List<int>{ 2, 3, 4, 5, 6, 7, 8, 9, 10, 16, 17, 27, 31, 62 }) {      ba = b; c = 0; foreach (var a in PG.Primes(lim))        if (nd(s = from10(a))) Write("{0,4} {1}", s, ++c % 20 == 0 ? "\n" : "");    WriteLine("\nBase {0}: found {1} non-decreasing primes under {2:n0}\n", b, c, from10(lim)); } } }  class PG { public static IEnumerable<int> Primes(int lim) {    var flags = new bool[lim + 1]; int j; yield return 2;    for (j = 4; j <= lim; j += 2) flags[j] = true; j = 3;    for (int d = 8, sq = 9; sq <= lim; j += 2, sq += d += 8)      if (!flags[j]) { yield return j;        for (int k = sq, i = j << 1; k <= lim; k += i) flags[k] = true; }    for (; j <= lim; j += 2) if (!flags[j]) yield return j; } }`
Output:
```  11  111 11111 1111111
Base 2: found 4 non-decreasing primes under 1111101000

2   12  111  122 1112 1222
Base 3: found 6 non-decreasing primes under 1101001

2    3   11   13   23  113  133  223  233 1223 1333 2333 11123 11233 11333 12233 22223
Base 4: found 17 non-decreasing primes under 33220

2    3   12   23   34  111  122  133 1112 1123 1233 1244 2223 2344 3444 11122 12222
Base 5: found 17 non-decreasing primes under 13000

2    3    5   11   15   25   35   45  111  115  125  135  155  225  245  255  335  345  445  455
1115 1125 1145 1235 1245 1335 1345 1355 1445 1555 2225 2335 2345 2555 3445 3455 3555
Base 6: found 37 non-decreasing primes under 4344

2    3    5   14   16   23   25   56  113  115  124  133  146  155  166  245  256  335  344  346
445  566 1112 1123 1136 1156 1222 1226 1235 1345 1444 1466 2234 2236 2333 2335 2366 2555
Base 7: found 38 non-decreasing primes under 2626

2    3    5    7   13   15   23   27   35   37   45   57  111  117  123  145  147  155  177  225
227  235  247  255  277  337  345  357  445  467  557  577  667 1113 1127 1137 1145 1167 1223 1225
1245 1335 1347 1357 1467 1555 1567
Base 8: found 47 non-decreasing primes under 1750

2    3    5    7   12   14   18   25   34   45   47   58   67   78  117  122  124  128  135  155
177  234  238  267  278  337  344  355  377  447  557  568  667  678  788 1112 1114 1118 1147 1158
1178 1222 1255 1268 1288
Base 9: found 45 non-decreasing primes under 1331

2    3    5    7   11   13   17   19   23   29   37   47   59   67   79   89  113  127  137  139
149  157  167  179  199  223  227  229  233  239  257  269  277  337  347  349  359  367  379  389
449  457  467  479  499  557  569  577  599  677
Base 10: found 50 non-decreasing primes under 1000

2    3    5    7    B    D   11   13   17   1D   1F   25   29   2B   2F   35   3B   3D   47   49
4F   59   67   6B   6D   7F   89   8B   9D   AD   BF   DF   EF  115  119  11B  125  133  137  139
13D  14B  15B  15D  167  16F  17B  17F  18D  199  1AF  1BB  1CD  1CF  1DF  223  22D  233  239  23B
24B  257  259  25F  269  26B  277  28D  2AB  2BD  2CF  2DD  2EF  335  337  33B  33D  347  355  359
35B  35F  36D  377  38B  38F  3AD  3DF
Base 16: found 88 non-decreasing primes under 3E8

2    3    5    7    B    D   12   16   1C   1E   23   27   29   2D   38   3A   3G   45   4B   4F
5C   5G   67   6B   78   7C   8D   8F   9A   9E   AB   BC   FG  111  115  117  11B  128  12E  137
139  13D  14A  14G  155  159  15F  166  16A  17B  17D  188  18E  19F  1BB  1BF  1CG  1DD  1EE  1GG
225  227  23C  23E  247  24D  24F  25A  25E  26B  27C  28D  29C  2AD  2CF  33B  346  34C  35F  368
36E  37B
Base 17: found 82 non-decreasing primes under 37E

2    3    5    7    B    D    H    J    N   12   14   1A   1E   1G   1K   1Q   25   27   2D   2H
2J   2P   38   3G   3K   3M   3Q   45   4J   4N   5E   5G   5M   6B   6H   6J   78   7A   7M   8B
8D   8H   8N   8P   9E   9K   9Q   AB   AD   AN   BE   BG   BK   CD   CN   CP   DG   DM   EJ   EN
FG   FQ   GH   GP   HK   IN   KN   LQ   MN   MP   NQ   OP   PQ  111  115  11D  11H  124  12E  12Q
13B  13D  13H  13J  14G  14K  14M  14Q  15D  15H  15J  15N  16G  16K  17B  17J  17N  188  18M  18Q
19B  19J  19P
Base 27: found 103 non-decreasing primes under 1A1

2    3    5    7    B    D    H    J    N    T   16   1A   1C   1G   1M   1S   1U   25   29   2B
2H   2L   2R   34   38   3A   3E   3G   3K   47   4D   4F   4P   4R   58   5C   5I   5O   5Q   67
6B   6D   6P   7A   7C   7G   7M   7O   89   8F   8L   8N   8T   9E   9S   AL   AR   BC   BI   BQ
CH   CP   CT   DG   DI   DS   DU   EF   EN   ER   ET   FM   FQ   GP   GR   HK   HU   IJ   IT   JO
JS   JU   KL   KN   KR   LM   LQ   MR   NQ   NU   OP   OT   TU  115
Base 31: found 94 non-decreasing primes under 118

2    3    5    7    B    D    H    J    N    T    V    b    f    h    l    r    x    z   15   19
1B   1H   1L   1R   1Z   1d   1f   1j   1l   1p   23   27   2D   2F   2P   2R   2X   2d   2h   2n
2t   2v   35   37   3B   3D   3P   3b   3f   3h   3l   3r   3t   49   4F   4L   4N   4T   4X   4Z
4j   4x   57   5L   5R   5b   5d   5h   5n   5v   67   6B   6H   6P   6T   6b   6l   6n   6x   6z
79   7F   7N   7R   7T   7X   7j   7r   7v   8D   8P   8R   8j   8p   8z   9B   9D   9J   9T   9Z
9f   9h   9n   9t   9x   9z   AB   AL   AN   AR   AX   Ad   Af   Ar   Av   BJ   BR   Bb   Bj   Bp
Bv   Bz   CD   CH   CP   CT   Ch   Cr   DF   DH   DL   DN   DX   Dl   Dp   Dr   Dv   EF   EJ   Ed
Eh   Ep   Ez   FH   FN   Fb   Ff   Fl   Fr   Fz
Base 62: found 150 non-decreasing primes under G8```

## F#

This task uses Extensible Prime Generator (F#)

` // Primes with digits in nondecreasing order: Nigel Galloway. May 16th., 2021let rec fN g=function n when n<10->(n<=g) |n when (n%10)<=g->fN(n%10)(n/10) |_->falselet fN=fN 9 in primes32()|>Seq.takeWhile((>)1000)|>Seq.filter fN|>Seq.iter(printf "%d "); printfn "" `
Output:
```2 3 5 7 11 13 17 19 23 29 37 47 59 67 79 89 113 127 137 139 149 157 167 179 199 223 227 229 233 239 257 269 277 337 347 349 359 367 379 389 449 457 467 479 499 557 569 577 599 677
```

## Factor

Works with: Factor version 0.99 2021-02-05
`USING: grouping lists lists.lazy math math.primes.listspresent prettyprint ; lprimes [ present [ <= ] monotonic? ] lfilter[ 1000 < ] lwhile [ . ] leach`
Output:
```2
3
5
7
11
13
17
19
23
29
37
47
59
67
79
89
113
127
137
139
149
157
167
179
199
223
227
229
233
239
257
269
277
337
347
349
359
367
379
389
449
457
467
479
499
557
569
577
599
677
```

## J

`echo (([:*./2<:/\10#.^:_1])"0#])@(i.&.(p:^:_1)) 1000exit 0`
Output:
`2 3 5 7 11 13 17 19 23 29 37 47 59 67 79 89 113 127 137 139 149 157 167 179 199 223 227 229 233 239 257 269 277 337 347 349 359 367 379 389 449 457 467 479 499 557 569 577 599 677`

## FreeBASIC

`#include "isprime.bas" function is_ndp( byval n as integer ) as boolean    'reads from the least significant digit first    dim as integer d=10, ld    do        ld = d        d = n mod 10        if d > ld then return false        n = n\10    loop until n = 0    return trueend function for i as uinteger = 2 to 999    if isprime(i) andalso is_ndp(i) then print i;" ";next i : print`
Output:
`2 3 5 7 11 13 17 19 23 29 37 47 59 67 79 89 113 127 137 139 149 157 167 179 199 223 227 229 233 239 257 269 277 337 347 349 359 367 379 389 449 457 467 479 499 557 569 577 599 677`

## Go

Translation of: Wren
Library: Go-rcu
`package main import (    "fmt"    "rcu") func nonDescending(p int) bool {    var digits []int    for p > 0 {        digits = append(digits, p%10)        p = p / 10    }    for i := 0; i < len(digits)-1; i++ {        if digits[i+1] > digits[i] {            return false        }    }    return true} func main() {    primes := rcu.Primes(999)    var nonDesc []int    for _, p := range primes {        if nonDescending(p) {            nonDesc = append(nonDesc, p)        }    }    fmt.Println("Primes below 1,000 with digits in non-decreasing order:")    for i, n := range nonDesc {        fmt.Printf("%3d ", n)        if (i+1)%10 == 0 {            fmt.Println()        }    }    fmt.Printf("\n%d such primes found.\n", len(nonDesc))}`
Output:
```Primes below 1,000 with digits in non-decreasing order:
2   3   5   7  11  13  17  19  23  29
37  47  59  67  79  89 113 127 137 139
149 157 167 179 199 223 227 229 233 239
257 269 277 337 347 349 359 367 379 389
449 457 467 479 499 557 569 577 599 677

50 such primes found.
```

## Julia

Translation of: Raku

Note for the case-sensitive digits base 62 example: Julia defaults to 'A' < 'a' in sorting. So Aa is in order, but aA is not nondecreasing.

`using Primes const range = 2:999 for base in [2:10...;[16, 17, 27, 31, 62]]    primes = filter(n -> isprime(n) && issorted(digits(n, base=base), rev=true), range)    println("\nBase \$base: ", length(primes), " non-descending primes between 1 and ",        string(last(primes), base=base), ":")    foreach(p -> print(lpad(string(p[2], base=base), 5), p[1] % 16 == 0 ? "\n" : ""), enumerate(primes))end `
Output:
```Base 2: 4 non-descending primes between 1 and 1111111:
11  111111111111111
Base 3: 6 non-descending primes between 1 and 1222:
2   12  111  122 1112 1222
Base 4: 17 non-descending primes between 1 and 22223:
2    3   11   13   23  113  133  223  233 1223 1333 233311123112331133312233
22223
Base 5: 17 non-descending primes between 1 and 12222:
2    3   12   23   34  111  122  133 1112 1123 1233 1244 2223 2344 344411122
12222
Base 6: 37 non-descending primes between 1 and 3555:
2    3    5   11   15   25   35   45  111  115  125  135  155  225  245  255
335  345  445  455 1115 1125 1145 1235 1245 1335 1345 1355 1445 1555 2225 2335
2345 2555 3445 3455 3555
Base 7: 38 non-descending primes between 1 and 2555:
2    3    5   14   16   23   25   56  113  115  124  133  146  155  166  245
256  335  344  346  445  566 1112 1123 1136 1156 1222 1226 1235 1345 1444 1466
2234 2236 2333 2335 2366 2555
Base 8: 47 non-descending primes between 1 and 1567:
2    3    5    7   13   15   23   27   35   37   45   57  111  117  123  145
147  155  177  225  227  235  247  255  277  337  345  357  445  467  557  577
667 1113 1127 1137 1145 1167 1223 1225 1245 1335 1347 1357 1467 1555 1567
Base 9: 45 non-descending primes between 1 and 1288:
2    3    5    7   12   14   18   25   34   45   47   58   67   78  117  122
124  128  135  155  177  234  238  267  278  337  344  355  377  447  557  568
667  678  788 1112 1114 1118 1147 1158 1178 1222 1255 1268 1288
Base 10: 50 non-descending primes between 1 and 677:
2    3    5    7   11   13   17   19   23   29   37   47   59   67   79   89
113  127  137  139  149  157  167  179  199  223  227  229  233  239  257  269
277  337  347  349  359  367  379  389  449  457  467  479  499  557  569  577
599  677
Base 16: 88 non-descending primes between 1 and 3df:
2    3    5    7    b    d   11   13   17   1d   1f   25   29   2b   2f   35
3b   3d   47   49   4f   59   67   6b   6d   7f   89   8b   9d   ad   bf   df
ef  115  119  11b  125  133  137  139  13d  14b  15b  15d  167  16f  17b  17f
18d  199  1af  1bb  1cd  1cf  1df  223  22d  233  239  23b  24b  257  259  25f
269  26b  277  28d  2ab  2bd  2cf  2dd  2ef  335  337  33b  33d  347  355  359
35b  35f  36d  377  38b  38f  3ad  3df
Base 17: 82 non-descending primes between 1 and 37b:
2    3    5    7    b    d   12   16   1c   1e   23   27   29   2d   38   3a
3g   45   4b   4f   5c   5g   67   6b   78   7c   8d   8f   9a   9e   ab   bc
fg  111  115  117  11b  128  12e  137  139  13d  14a  14g  155  159  15f  166
16a  17b  17d  188  18e  19f  1bb  1bf  1cg  1dd  1ee  1gg  225  227  23c  23e
247  24d  24f  25a  25e  26b  27c  28d  29c  2ad  2cf  33b  346  34c  35f  368
36e  37b
Base 27: 103 non-descending primes between 1 and 19p:
2    3    5    7    b    d    h    j    n   12   14   1a   1e   1g   1k   1q
25   27   2d   2h   2j   2p   38   3g   3k   3m   3q   45   4j   4n   5e   5g
5m   6b   6h   6j   78   7a   7m   8b   8d   8h   8n   8p   9e   9k   9q   ab
ad   an   be   bg   bk   cd   cn   cp   dg   dm   ej   en   fg   fq   gh   gp
hk   in   kn   lq   mn   mp   nq   op   pq  111  115  11d  11h  124  12e  12q
13b  13d  13h  13j  14g  14k  14m  14q  15d  15h  15j  15n  16g  16k  17b  17j
17n  188  18m  18q  19b  19j  19p
Base 31: 94 non-descending primes between 1 and 115:
2    3    5    7    b    d    h    j    n    t   16   1a   1c   1g   1m   1s
1u   25   29   2b   2h   2l   2r   34   38   3a   3e   3g   3k   47   4d   4f
4p   4r   58   5c   5i   5o   5q   67   6b   6d   6p   7a   7c   7g   7m   7o
89   8f   8l   8n   8t   9e   9s   al   ar   bc   bi   bq   ch   cp   ct   dg
di   ds   du   ef   en   er   et   fm   fq   gp   gr   hk   hu   ij   it   jo
js   ju   kl   kn   kr   lm   lq   mr   nq   nu   op   ot   tu  115
Base 62: 150 non-descending primes between 1 and Fz:
2    3    5    7    B    D    H    J    N    T    V    b    f    h    l    r
x    z   15   19   1B   1H   1L   1R   1Z   1d   1f   1j   1l   1p   23   27
2D   2F   2P   2R   2X   2d   2h   2n   2t   2v   35   37   3B   3D   3P   3b
3f   3h   3l   3r   3t   49   4F   4L   4N   4T   4X   4Z   4j   4x   57   5L
5R   5b   5d   5h   5n   5v   67   6B   6H   6P   6T   6b   6l   6n   6x   6z
79   7F   7N   7R   7T   7X   7j   7r   7v   8D   8P   8R   8j   8p   8z   9B
9D   9J   9T   9Z   9f   9h   9n   9t   9x   9z   AB   AL   AN   AR   AX   Ad
Af   Ar   Av   BJ   BR   Bb   Bj   Bp   Bv   Bz   CD   CH   CP   CT   Ch   Cr
DF   DH   DL   DN   DX   Dl   Dp   Dr   Dv   EF   EJ   Ed   Eh   Ep   Ez   FH
FN   Fb   Ff   Fl   Fr   Fz
```

## MAD

`            NORMAL MODE IS INTEGER            BOOLEAN PRIME            DIMENSION PRIME(1000), COL(10)            PRIME(0) = 0B            PRIME(1) = 0B            SQMAX=SQRT.(1000)            THROUGH INIT, FOR I=2, 1, I.G.1000INIT        PRIME(I) = 1B            THROUGH SIEVE, FOR I=2, 1, I.G.SQMAX            WHENEVER PRIME(I)                THROUGH SIEVE2, FOR J=I+I, I, J.G.1000SIEVE2          PRIME(J) = 0B            END OF CONDITIONALSIEVE       CONTINUE            C = 1            THROUGH TEST, FOR D100=0, 1, D100.G.9            THROUGH TEST, FOR D10=D100, 1, D10.G.9            THROUGH TEST, FOR D1=D10, 1, D1.G.9            N = D100*100+D10*10+D1            WHENEVER PRIME(N)                COL(C) = N                C = C+1                WHENEVER C.G.10                    PRINT FORMAT CFMT,COL(1),COL(2),COL(3),COL(4),          0               COL(5),COL(6),COL(7),COL(8),COL(9),COL(10)                    C = 1                END OF CONDITIONAL            END OF CONDITIONALTEST        CONTINUE            VECTOR VALUES CFMT = \$10(I4)*\$            END OF PROGRAM `
Output:
```   2   3   5   7  11  13  17  19  23  29
37  47  59  67  79  89 113 127 137 139
149 157 167 179 199 223 227 229 233 239
257 269 277 337 347 349 359 367 379 389
449 457 467 479 499 557 569 577 599 677```

## Nim

`import strformat, sugar func isPrime(n: Natural): bool =  if n < 2: return false  if n mod 2 == 0: return n == 2  if n mod 3 == 0: return n == 3  var d = 5  while d * d <= n:    if n mod d == 0: return false    inc d, 2    if n mod d == 0: return false    inc d, 4  result = true func isNonDecreasing(n: int): bool =  var n = n  var prev = 10  while n != 0:    let d = n mod 10    if d > prev: return false    prev = d    n = n div 10  result = true let result = collect(newSeq):               for n in 2..999:                 if n.isPrime and n.isNonDecreasing: n echo &"Found {result.len} primes:"for i, n in result:  stdout.write &"{n:3}", if (i + 1) mod 10 == 0: '\n' else: ' '`
Output:
```Found 50 primes:
2   3   5   7  11  13  17  19  23  29
37  47  59  67  79  89 113 127 137 139
149 157 167 179 199 223 227 229 233 239
257 269 277 337 347 349 359 367 379 389
449 457 467 479 499 557 569 577 599 677```

## Phix

```function nd(string s) return s=sort(s) end function
sequence res = filter(apply(true,sprintf,{{"%d"},get_primes_le(1000)}),nd)
printf(1,"%d non-decreasing primes < 1,000: %s\n",{length(res),join(shorten(res,"",5))})
```
Output:
```50 non-decreasing primes < 1,000: 2 3 5 7 11 ... 557 569 577 599 677
```

## Perl

Library: ntheory
`#!/usr/bin/perl use strict;use warnings;use ntheory qw( primes ); my @want = grep ! /(.)(.)(??{\$1 > \$2 ? '' : '(*FAIL)'})/, @{ primes(1000) };print "@want" =~ s/.{50}\K /\n/gr . "\n\ncount: " . @want . "\n";`
Output:
```2 3 5 7 11 13 17 19 23 29 37 47 59 67 79 89 113 127
137 139 149 157 167 179 199 223 227 229 233 239 257
269 277 337 347 349 359 367 379 389 449 457 467 479
499 557 569 577 599 677

count: 50
```

## Plain English

`To run:Start up.Loop.If a counter is past 1000, break.If the counter is prime and non-decreasing, write the counter then " " on the console without advancing.Repeat.Wait for the escape key.Shut down. To decide if a number is non-decreasing:Privatize the number.Put 10 into a previous digit number.Loop.Divide the number by 10 giving a quotient and a remainder.If the remainder is greater than the previous digit, say no.Put the remainder into the previous digit.Put the quotient into the number.If the number is 0, say yes.Repeat. To decide if a number is prime and non-decreasing:If the number is not prime, say no.If the number is not non-decreasing, say no.Say yes.`
Output:
```2 3 5 7 11 13 17 19 23 29 37 47 59 67 79 89 113 127 137 139 149 157 167 179 199 223 227 229 233 239 257 269 277 337 347 349 359 367 379 389 449 457 467 479 499 557 569 577 599 677
```

## PL/M

`100H:BDOS: PROCEDURE (FN, ARG); DECLARE FN BYTE, ARG ADDRESS; GO TO 5; END BDOS;EXIT: PROCEDURE; CALL BDOS(0,0); END EXIT;PRINT: PROCEDURE (S); DECLARE S ADDRESS; CALL BDOS(9,S); END PRINT; PRINT\$NUMBER: PROCEDURE (N);    DECLARE S (6) BYTE INITIAL ('.....\$');    DECLARE (N, P) ADDRESS, C BASED P BYTE;    P = .S(5);DIGIT:    P = P - 1;    C = N MOD 10 + '0';    N = N / 10;    IF N > 0 THEN GO TO DIGIT;    CALL PRINT(P);END PRINT\$NUMBER; SIEVE: PROCEDURE (MAX, PBASE);    DECLARE (MAX, PBASE) ADDRESS, P BASED PBASE BYTE;    DECLARE (I, J) ADDRESS;    P(0)=0;    P(1)=0;    DO I=2 TO MAX; P(I)=1; END;    DO I=2 TO MAX/2;        IF P(I) THEN            DO J=I+I TO MAX BY I;                P(J)=0;            END;    END;END SIEVE; DECLARE (D\$100, D\$10, D\$1, COL) BYTE;DECLARE P (1000) BYTE;DECLARE N ADDRESS;CALL SIEVE(LAST(P), .P); COL = 0;DO D\$100 = 0 TO 9;    DO D\$10 = D\$100 TO 9;        DO D\$1 = D\$10 TO 9;            N = D\$100*100 + D\$10*10 + D\$1;            IF P(N) THEN DO;                CALL PRINT\$NUMBER(N);                IF COL < 9 THEN DO;                    COL = COL + 1;                    CALL PRINT(.(9,36));                END;                ELSE DO;                    COL = 0;                    CALL PRINT(.(13,10,36));                END;            END;        END;    END;END;CALL EXIT;EOF`
Output:
```2       3       5       7       11      13      17      19      23      29
37      47      59      67      79      89      113     127     137     139
149     157     167     179     199     223     227     229     233     239
257     269     277     337     347     349     359     367     379     389
449     457     467     479     499     557     569     577     599     677```

## Python

`'''Primes with monotonic (rising or equal) digits''' from operator import lefrom itertools import takewhile  # monotonicDigits :: Int -> Int -> Booldef monotonicDigits(base):    '''True if the decimal digits of n       are monotonic under (<=)    '''    def go(n):        return monotonic(le)(            showIntAtBase(base)(digitFromInt)(n)('')        )    return go  # monotonic :: (a -> a -> Bool) -> [a] -> Booldef monotonic(op):    '''True if the op returns True for each       successive pair of values in xs.    '''    def go(xs):        return all(map(op, xs, xs[1:]))    return go  # ------------------------- TEST -------------------------# main :: IO ()def main():    '''Primes below 1000 in which any decimal digit is       lower than or equal to any digit to its right.    '''    xs = [        str(n) for n in takewhile(            lambda n: 1000 > n,            filter(monotonicDigits(10), primes())        )    ]    w = len(xs[-1])    print(f'{len(xs)} matches for base 10:\n')    print('\n'.join(        ' '.join(row) for row in chunksOf(10)([            x.rjust(w, ' ') for x in xs        ])    ))  # ----------------------- GENERIC ------------------------ # chunksOf :: Int -> [a] -> [[a]]def chunksOf(n):    '''A series of lists of length n, subdividing the       contents of xs. Where the length of xs is not evenly       divible, the final list will be shorter than n.    '''    def go(xs):        return (            xs[i:n + i] for i in range(0, len(xs), n)        ) if 0 < n else None    return go  # digitFromInt :: Int -> Chardef digitFromInt(n):    '''A character representing a small       integer value.    '''    return '0123456789abcdefghijklmnopqrstuvwxyz'[n] if (        0 <= n < 36    ) else '?'  # primes :: [Int]def primes():    ''' Non finite sequence of prime numbers.    '''    n = 2    dct = {}    while True:        if n in dct:            for p in dct[n]:                dct.setdefault(n + p, []).append(p)            del dct[n]        else:            yield n            dct[n * n] = [n]        n = 1 + n  # showIntAtBase :: Int -> (Int -> Char) -> Int -># String -> Stringdef showIntAtBase(base):    '''String representation of an integer in a given base,       using a supplied function for the string       representation of digits.    '''    def wrap(toChr, n, rs):        def go(nd, r):            n, d = nd            r_ = toChr(d) + r            return go(divmod(n, base), r_) if 0 != n else r_        return 'unsupported base' if 1 >= base else (            'negative number' if 0 > n else (                go(divmod(n, base), rs))        )    return lambda toChr: lambda n: lambda rs: (        wrap(toChr, n, rs)    )  # MAIN ---if __name__ == '__main__':    main() `
Output:
```50 matches for base 10:

2   3   5   7  11  13  17  19  23  29
37  47  59  67  79  89 113 127 137 139
149 157 167 179 199 223 227 229 233 239
257 269 277 337 347 349 359 367 379 389
449 457 467 479 499 557 569 577 599 677```

## Raku

`my \$range = ^1000; for flat 2..10, 17, 27, 31 -> \$base {   say "\nBase \$base: {+\$_} non-decending primes between \$range.minmax.map( *.base: \$base ).join(' and '):\n{      .batch(20)».fmt("%{.tail.chars}s").join: "\n" }"       given \$range.grep( *.is-prime ).map( *.base: \$base ).grep: { [le] .comb }}`
Output:
```Base 2: 4 non-decending primes between 0 and 1111100111:
11     111   11111 1111111

Base 3: 6 non-decending primes between 0 and 1101000:
2   12  111  122 1112 1222

Base 4: 17 non-decending primes between 0 and 33213:
2     3    11    13    23   113   133   223   233  1223  1333  2333 11123 11233 11333 12233 22223

Base 5: 17 non-decending primes between 0 and 12444:
2     3    12    23    34   111   122   133  1112  1123  1233  1244  2223  2344  3444 11122 12222

Base 6: 37 non-decending primes between 0 and 4343:
2    3    5   11   15   25   35   45  111  115  125  135  155  225  245  255  335  345  445  455
1115 1125 1145 1235 1245 1335 1345 1355 1445 1555 2225 2335 2345 2555 3445 3455 3555

Base 7: 38 non-decending primes between 0 and 2625:
2    3    5   14   16   23   25   56  113  115  124  133  146  155  166  245  256  335  344  346
445  566 1112 1123 1136 1156 1222 1226 1235 1345 1444 1466 2234 2236 2333 2335 2366 2555

Base 8: 47 non-decending primes between 0 and 1747:
2    3    5    7   13   15   23   27   35   37   45   57  111  117  123  145  147  155  177  225
227  235  247  255  277  337  345  357  445  467  557  577  667 1113 1127 1137 1145 1167 1223 1225
1245 1335 1347 1357 1467 1555 1567

Base 9: 45 non-decending primes between 0 and 1330:
2    3    5    7   12   14   18   25   34   45   47   58   67   78  117  122  124  128  135  155
177  234  238  267  278  337  344  355  377  447  557  568  667  678  788 1112 1114 1118 1147 1158
1178 1222 1255 1268 1288

Base 10: 50 non-decending primes between 0 and 999:
2   3   5   7  11  13  17  19  23  29  37  47  59  67  79  89 113 127 137 139
149 157 167 179 199 223 227 229 233 239 257 269 277 337 347 349 359 367 379 389
449 457 467 479 499 557 569 577 599 677

Base 17: 82 non-decending primes between 0 and 37D:
2   3   5   7   B   D  12  16  1C  1E  23  27  29  2D  38  3A  3G  45  4B  4F
5C  5G  67  6B  78  7C  8D  8F  9A  9E  AB  BC  FG 111 115 117 11B 128 12E 137
139 13D 14A 14G 155 159 15F 166 16A 17B 17D 188 18E 19F 1BB 1BF 1CG 1DD 1EE 1GG
225 227 23C 23E 247 24D 24F 25A 25E 26B 27C 28D 29C 2AD 2CF 33B 346 34C 35F 368
36E 37B

Base 27: 103 non-decending primes between 0 and 1A0:
2   3   5   7   B   D   H   J   N  12  14  1A  1E  1G  1K  1Q  25  27  2D  2H
2J  2P  38  3G  3K  3M  3Q  45  4J  4N  5E  5G  5M  6B  6H  6J  78  7A  7M  8B
8D  8H  8N  8P  9E  9K  9Q  AB  AD  AN  BE  BG  BK  CD  CN  CP  DG  DM  EJ  EN
FG  FQ  GH  GP  HK  IN  KN  LQ  MN  MP  NQ  OP  PQ 111 115 11D 11H 124 12E 12Q
13B 13D 13H 13J 14G 14K 14M 14Q 15D 15H 15J 15N 16G 16K 17B 17J 17N 188 18M 18Q
19B 19J 19P

Base 31: 94 non-decending primes between 0 and 117:
2   3   5   7   B   D   H   J   N   T  16  1A  1C  1G  1M  1S  1U  25  29  2B
2H  2L  2R  34  38  3A  3E  3G  3K  47  4D  4F  4P  4R  58  5C  5I  5O  5Q  67
6B  6D  6P  7A  7C  7G  7M  7O  89  8F  8L  8N  8T  9E  9S  AL  AR  BC  BI  BQ
CH  CP  CT  DG  DI  DS  DU  EF  EN  ER  ET  FM  FQ  GP  GR  HK  HU  IJ  IT  JO
JS  JU  KL  KN  KR  LM  LQ  MR  NQ  NU  OP  OT  TU 115```

## REXX

`/*REXX program finds & displays primes whose decimal digits are in non─decreasing order.*/parse arg n cols .                               /*obtain optional argument from the CL.*/if    n=='' |    n==","  then    n= 1000         /*Not specified?  Then use the default.*/if cols=='' | cols==","  then cols=   10         /* "      "         "   "   "     "    */call genP                                        /*build array of semaphores for primes.*/w= 10                                            /*width of a number in any column.     */                                     title= ' primes whose decimal digits are in'     ,                                            'non─decreasing order,  N  < '   commas(n)if cols>0  then say ' index │'center(title,   1 + cols*(w+1)     )if cols>0  then say '───────┼'center(""   ,   1 + cols*(w+1), '─')found= 0;                    idx= 1              /*initialize # of non─decreasing primes*/\$=                                               /*a list of non─decreasing digit primes*/     do j=1  while @.j<n;   p= @.j              /*examine the primes within the range. */        do k=1  for length(p)-1                  /*validate that it meets specifications*/        if substr(p, k, 1) > substr(p, k+1, 1)  then iterate j  /*compare dig with next.*/        end   /*k*/     found= found + 1                            /*bump number of non─decreasing primes.*/     if cols<0             then iterate          /*Just do the summary?  Then skip grid.*/     \$= \$ right( commas(j), w)                   /*add a commatized prime──►list (grid).*/     if found//cols\==0    then iterate          /*have we populated a line of output?  */     say center(idx, 7)'│'  substr(\$, 2);   \$=   /*display what we have so far  (cols). */     idx= idx + cols                             /*bump the  index  count for the output*/     end   /*j*/ if \$\==''  then say center(idx, 7)"│"  substr(\$, 2)  /*possible display residual output.*/if cols>0  then say '───────┴'center(""    ,   1 + cols*(w+1), '─') /*display foot sep. */saysay 'Found '       commas(found)       title                        /*display foot title*/exit 0                                           /*stick a fork in it,  we're all done. *//*──────────────────────────────────────────────────────────────────────────────────────*/commas: parse arg ?;  do jc=length(?)-3  to 1  by -3; ?=insert(',', ?, jc); end;  return ?/*──────────────────────────────────────────────────────────────────────────────────────*/genP: @.1=2;  @.2=3;  @.3=5;  @.4=7              /*define some low primes.              */               #= 3;                s.#= @.# **2 /*number of primes so far;     prime². */                                                 /* [↓]  generate more  primes  ≤  high.*/        do [email protected].#+2  by 2  to n-1                 /*find odd primes from here on.        */        parse var j '' -1 _; if     _==5  then iterate  /*J divisible by 5?  (right dig)*/                             if j// 3==0  then iterate  /*"     "      " 3?             */                                                 /* [↑]  the above five lines saves time*/               do k=4  while s.k<=j              /* [↓]  divide by the known odd primes.*/               if j // @.k == 0  then iterate j  /*Is  J ÷ X?  Then not prime.     ___  */               end   /*k*/                       /* [↑]  only process numbers  ≤  √ J   */        #= #+1;    @.#= j;    s.#= j*j           /*bump # of Ps; assign next P;  P²; P# */        end          /*j*/;   return`
output   when using the default inputs:
``` index │                     primes whose decimal digits are in non─decreasing order,  N  <  1,000
───────┼───────────────────────────────────────────────────────────────────────────────────────────────────────────────
1   │          1          2          3          4          5          6          7          8          9         10
11   │         12         15         17         19         22         24         30         31         33         34
21   │         35         37         39         41         46         48         49         50         51         52
31   │         55         57         59         68         69         70         72         73         75         77
41   │         87         88         91         92         95        102        104        106        109        123
───────┴───────────────────────────────────────────────────────────────────────────────────────────────────────────────

Found  50  primes whose decimal digits are in non─decreasing order,  N  <  1,000
```

## Ring

`load "stdlib.ring" ? "working..." c = 0limit = 1000 ? "Primes under " + limit + " with digits in nondecreasing order:" for n = 1 to limit    flag = 1    strn = string(n)    if isprime(n)        for m = 1 to len(strn) - 1            if strn[m] > strn[m + 1]               flag = 0               exit            ok        next        if flag = 1           see sf(n, 4) + " "           c++ if c % 10 = 0 see nl ok        ok    oknext ? nl + "Found " + c + " base 10 primes with digits in nondecreasing order"? "done..." # a very plain string formatter, intended to even up columnar outputsdef sf x, y    s = string(x) l = len(s)    if l > y y = l ok    return substr("          ", 11 - y + l) + s`
Output:
```working...
Primes under 1000 with digits in nondecreasing order:
2    3    5    7   11   13   17   19   23   29
37   47   59   67   79   89  113  127  137  139
149  157  167  179  199  223  227  229  233  239
257  269  277  337  347  349  359  367  379  389
449  457  467  479  499  557  569  577  599  677

Found 50 base 10 primes with digits in nondecreasing order
done...```

## Seed7

`\$ include "seed7_05.s7i";  const func boolean: isPrime (in integer: number) is func  result    var boolean: prime is FALSE;  local    var integer: upTo is 0;    var integer: testNum is 3;  begin    if number = 2 then      prime := TRUE;    elsif odd(number) and number > 2 then      upTo := sqrt(number);      while number rem testNum <> 0 and testNum <= upTo do        testNum +:= 2;      end while;      prime := testNum > upTo;    end if;  end func;  const func boolean: isNondecreasing (in var integer: number) is func  result    var boolean: nondecreasing is TRUE;  local    var integer: previousDigit is 10;    var integer: currentDigit is 0;  begin    while number <> 0 and nondecreasing do      currentDigit := number rem 10;      if currentDigit > previousDigit then        nondecreasing := FALSE;      end if;      number := number div 10;      previousDigit := currentDigit;    end while;  end func;  const proc: main is func  local    var integer: n is 0;  begin    write("2 ");    for n range 3 to 999 step 2 do      if isPrime(n) and isNondecreasing(n) then        write(n <& " ");      end if;    end for;  end func;`
Output:
```2 3 5 7 11 13 17 19 23 29 37 47 59 67 79 89 113 127 137 139 149 157 167 179 199 223 227 229 233 239 257 269 277 337 347 349 359 367 379 389 449 457 467 479 499 557 569 577 599 677
```

## Sidef

Simple solution:

`say 1000.primes.grep { .digits.cons(2).all { .head >= .tail } }`

Generate such primes from digits (asymptotically faster):

`func primes_with_nondecreasing_digits(upto, base = 10) {     upto = prev_prime(upto+1)     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 .. upto.ilog(base)) {        digits.combinations_with_repetition(k, {|*a|            var v = a.digits2num(base)            next if (v*base + end_digits.tail > upto)            end_digits.each {|d|                var n = (v*base + d)                next if ((n >= base) && (a[0] > d))                list << n if n.is_prime            }        })    }     list.sort} say primes_with_nondecreasing_digits(1000)`
Output:
```[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 37, 47, 59, 67, 79, 89, 113, 127, 137, 139, 149, 157, 167, 179, 199, 223, 227, 229, 233, 239, 257, 269, 277, 337, 347, 349, 359, 367, 379, 389, 449, 457, 467, 479, 499, 557, 569, 577, 599, 677]
```

## Visual Basic .NET

Translation of: C#
`Imports System.LinqImports System.Collections.GenericImports System.ConsoleImports System.Math Module Module1    Dim ba As Integer    Dim chars As String = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"     Iterator Function Primes(ByVal lim As Integer) As IEnumerable(Of Integer)        Dim flags(lim) As Boolean, j As Integer : Yield 2        For j = 4 To lim Step 2 : flags(j) = True : Next : j = 3        Dim d As Integer = 8, sq As Integer = 9        While sq <= lim            If Not flags(j) Then                Yield j : Dim i As Integer = j << 1                For k As Integer = sq To lim step i : flags(k) = True : Next            End If            j += 2 : d += 8 : sq += d : End While        While j <= lim            If Not flags(j) Then Yield j            j += 2 : End While    End Function     ' convert an int into a string using the current ba    Function from10(ByVal b As Integer) As String        Dim res As String = "", re As Integer        While b > 0 : b = DivRem(b, ba, re) : res = chars(CByte(re)) & res : End While : Return res    End Function     ' parse a string into an int, using current ba (not used here)    Function to10(ByVal s As String) As Integer        Dim res As Integer = 0        For Each i As Char In s : res = res * ba + chars.IndexOf(i) : Next : Return res    End Function     ' note: comparing the index of the chars instead of the chars themsleves, which avoids case issues    Function nd(ByVal s As String) As Boolean        If s.Length < 2 Then Return True        Dim l As Char = s(0)        For i As Integer = 1 To s.Length - 1            If chars.IndexOf(l) > chars.IndexOf(s(i)) Then Return False Else l = s(i)        Next : Return True    End Function     Sub Main(ByVal args As String())        Dim c As Integer, lim As Integer = 1000, s As String        For Each b As Integer In New List(Of Integer) From { 2, 3, 4, 5, 6, 7, 8, 9, 10, 16, 17, 27, 31, 62 }            ba = b : c = 0 : For Each a As Integer In Primes(lim)                s = from10(a) : If nd(s) Then c += 1 : Write("{0,4} {1}", s, If(c Mod 20 = 0, vbLf, ""))            Next            WriteLine(vbLf & "Base {0}: found {1} non-decreasing primes under {2:n0}" & vbLf, b, c, from10(lim))        Next    End SubEnd Module`
Output:

Same as C#.

## Wren

Library: Wren-math
Library: Wren-seq
Library: Wren-fmt
`import "/math" for Intimport "/seq" for Lstimport "/fmt" for Fmt var nonDescending = Fn.new { |p|    var digits = []    while (p > 0) {        digits.add(p % 10)        p = (p/10).floor    }    for (i in 0...digits.count-1) {        if (digits[i+1] > digits[i]) return false    }    return true} var primes = Int.primeSieve(999)var nonDesc = []for (p in primes) if (nonDescending.call(p)) nonDesc.add(p)System.print("Primes below 1,000 with digits in non-decreasing order:")for (chunk in Lst.chunks(nonDesc, 10)) Fmt.print("\$3d", chunk)System.print("\n%(nonDesc.count) such primes found.")`
Output:
```Primes below 1,000 with digits in non-decreasing order:
2   3   5   7  11  13  17  19  23  29
37  47  59  67  79  89 113 127 137 139
149 157 167 179 199 223 227 229 233 239
257 269 277 337 347 349 359 367 379 389
449 457 467 479 499 557 569 577 599 677

50 such primes found.
```

## XPL0

`func IsPrime(N);        \Return 'true' if N is a prime numberint  N, I;[if N <= 1 then return false;for I:= 2 to sqrt(N) do    if rem(N/I) = 0 then return false;return true;]; func Nondecreasing(N);\Return 'true' if N has left-to-right nondecreasing digits\Or return 'true' if N has right-to-left nonincreasing digitsint N, D, D0;[N:= N/10;D0:= rem(0);while N do    [N:= N/10;    D:= rem(0);    if D > D0 then return false;    D0:= D;    ];return true;]; int Count, N;[Count:= 0;for N:= 0 to 1000-1 do    if IsPrime(N) and Nondecreasing(N) then        [IntOut(0, N);        Count:= Count+1;        if rem(Count/10) = 0 then CrLf(0) else ChOut(0, 9\tab\);        ];CrLf(0);IntOut(0, Count);Text(0, " primes found with nondecreasing digits below 1000.");]`
Output:
```2       3       5       7       11      13      17      19      23      29
37      47      59      67      79      89      113     127     137     139
149     157     167     179     199     223     227     229     233     239
257     269     277     337     347     349     359     367     379     389
449     457     467     479     499     557     569     577     599     677

50 primes found with nondecreasing digits below 1000.
```