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# 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

## 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    ODEND`
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.AWKBEGIN {    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
```

## 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.functionsmath.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
```

## 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.

`   extend=: {{ y;(1+each i._1+{.y),L:0 y }}   \$(#~ 1 p: ])10#.&>([:[email protected];extend each)^:# >:i.9100   10 10\$(#~ 1 p: ])10#.&>([:[email protected];extend each)^:# >:i.9     2      3     13     23       5       7      17      37       47       67   127    137    347    157     257     457     167     367      467     1237  2347   2357   3457   1367    2467    3467    1567    4567    12347    12457 13457  13567  23567 123457  124567      19      29      59       79       89   139    239    149    349     359     269     569     179      379      479   389   1249   1259   1459    2459    3469    1279    1579     2579     4679  1289   2389   1489   2689    5689    1789    2789    4789    23459    13469 12569  12379  12479  13679   34679   15679   25679   12589    34589    12689 23689  13789  23789 123479  124679  235679  145679  345679   234589   345689134789 125789 235789 245789 1245689 1234789 1235789 1456789 12356789 23456789   timex'(#~ 1 p: ])10#.&>([:[email protected];extend each)^:# >:i.9' NB. seconds (take with grain of salt)0.003818 `

cpu here was a 1.2ghz i3-1005g1

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

## Mathematica/Wolfram Language

`[email protected][FromDigits /@ Subsets[[email protected], {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```

## Perl

`#!/usr/bin/perl use strict; # https://rosettacode.org/wiki/Ascending_primesuse warnings;use ntheory qw( 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}
{}
```

## 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```

## 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

 This example is incorrect. Please fix the code and remove this message.Details: Many of the numbers shown do not have strictly ascending digits, e.g. all the ones starting with 9. The single digit primes should also be included.
` load "stdlibcore.ring" limit = 1000row = 0 for n = 1 to limit    flag = 0    strn = string(n)    if isprime(n) = 1       for m = 1 to len(strn)-1           if number(substr(strn,m)) > number(substr(strn,m+1))              flag = 1           ok       next       if flag = 1          row++          see "" + n + " "       ok       if row % 10 = 0          see nl       ok    oknext `

Output:

11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997

## 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
```

## 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 Intimport "./seq"  for Lstimport "./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)ascPrimes.addAll(higherPrimes)System.print("There are %(ascPrimes.count) ascending primes, namely:")for (chunk in Lst.chunks(ascPrimes, 10)) Fmt.print("\$8d", chunk)`
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 Setimport "./math" for Intimport "./seq" for Lstimport "./fmt" for Fmt var ascPrimes = Set.new() // avoids duplicates var generate  // recursive functiongenerate = Fn.new { |first, cand, digits|    if (digits == 0) {        if (Int.isPrime(cand)) ascPrimes.add(cand)        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.toListascPrimes.sort()System.print("There are %(ascPrimes.count) ascending primes, namely:")for (chunk in Lst.chunks(ascPrimes, 10)) Fmt.print("\$8s", chunk)`
Output:
```Same as before.
```

## XPL0

Brute force solution: 4.3 seconds on Pi4.

`func IsPrime(N);        \Return 'true' if N is primeint  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 ascendingint  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;    while Mask do        [if Mask&1 then             N:= N*10 + Digit;        Mask:= Mask>>1;        Digit:= Digit+1;        ];    A(I):= N;    ];Sort(A, 512);Cnt:= 0;Format(9, 0);for I:= 1 to 511 do     \skip empty set    [N:= A(I);    if IsPrime(N) then        [RlOut(0, float(N));        Cnt:= Cnt+1;        if rem(Cnt/10) = 0 then CrLf(0);        ];    ];]`
Output:
```Same as before.
```