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Primes with digits in nondecreasing order

From Rosetta Code
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   n   primes with digits in non-decreasing order,   where   n   <   1000

ALGOL 68[edit]

BEGIN # find primes where the digits are non-descending #
INT max number = 1000;
# sieve the primes to max number #
[ 1 : max number ]BOOL prime;
prime[ 1 ] := FALSE; prime[ 2 ] := TRUE;
FOR i FROM 3 BY 2 TO max number DO prime[ i ] := TRUE OD;
FOR i FROM 4 BY 2 TO max number DO prime[ i ] := FALSE OD;
FOR i FROM 3 BY 2 TO ENTIER sqrt( max number ) DO
IF prime[ i ] THEN
FOR s FROM i * i BY i + i TO max number DO prime[ s ] := FALSE OD
FI
OD;
# 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

AWK[edit]

 
# syntax: GAWK -f PRIMES_WITH_DIGITS_IN_NONDECREASING_ORDER.AWK
BEGIN {
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

C#[edit]

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

Factor[edit]

Works with: Factor version 0.99 2021-02-05
USING: grouping lists lists.lazy math math.primes.lists
present 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

Julia[edit]

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

Phix[edit]

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

Raku[edit]

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[edit]

/*REXX program finds & displays primes whose decimal digits are in non─decreasing order.*/
parse arg hi cols . /*obtain optional argument from the CL.*/
if hi=='' | hi=="," then hi= 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. */
@ndcps= ' primes whose decimal digits are in non─decreasing order that' ,
'are < ' commas(hi)
if cols>0 then say ' index │'center(@ndcps, 1 + cols*(w+1) )
if cols>0 then say '───────┼'center("" , 1 + cols*(w+1), '─')
ndcps= 0; idx= 1 /*initialize # of non─decreasing primes*/
$= /*a list of non─decreasing digit primes*/
do j=1 while @.j<hi; 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*/
ndcps= ndcps + 1 /*bump number of non─decreasing primes.*/
if cols==0 then iterate /*Build the list (to be shown later)? */
c= commas(p) /*maybe add commas to the number. */
$= $ right(c, max(w, length(c) ) ) /*add a prime ──► list, allow big nums.*/
if ndcps//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.*/
say
say 'Found ' commas(ndcps) @ndcps
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 hi /*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 that are  <  1,000
───────┼───────────────────────────────────────────────────────────────────────────────────────────────────────────────
   1   │          2          3          5          7         11         13         17         19         23         29
  11   │         37         47         59         67         79         89        113        127        137        139
  21   │        149        157        167        179        199        223        227        229        233        239
  31   │        257        269        277        337        347        349        359        367        379        389
  41   │        449        457        467        479        499        557        569        577        599        677

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

Ring[edit]

load "stdlib.ring"
 
? "working..."
 
c = 0
limit = 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
ok
next
 
? nl + "Found " + c + " base 10 primes with digits in nondecreasing order"
? "done..."
 
# a very plain string formatter, intended to even up columnar outputs
def 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...

Visual Basic .NET[edit]

Translation of: C#
Imports System.Linq
Imports System.Collections.Generic
Imports System.Console
Imports 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 Sub
End Module
Output:

Same as C#.

Wren[edit]

Library: Wren-math
Library: Wren-seq
Library: Wren-fmt
import "/math" for Int
import "/seq" for Lst
import "/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.