Descending primes

Generate and show all primes with strictly descending decimal digits.

See also

OEIS:A052014 - Primes with distinct digits in descending order

Related

Ascending primes

Phix

with javascript_semantics
function descending_primes(sequence res, atom p=0)
    for d=(p==0) to iff(p=0?9:remainder(p,10)-1) do
        atom np = p*10+d
        if odd(d) and is_prime(np) then res &= np end if
        res = descending_primes(res,np)
    end for
    return res
end function
 
sequence r = sort(descending_primes({2})),
--sequence r = descending_primes({2}),
         j = join_by(r,1,11," ","\n","%8d")
printf(1,"There are %,d descending primes:\n%s\n",{length(r),j})

Output:

There are 87 descending primes:
       2        3        5        7       31       41       43       53       61       71       73
      83       97      421      431      521      541      631      641      643      653      743
     751      761      821      853      863      941      953      971      983     5431     6421
    6521     7321     7541     7621     7643     8431     8521     8543     8641     8731     8741
    8753     8761     9421     9431     9521     9631     9643     9721     9743     9851     9871
   75431    76421    76541    76543    86531    87421    87541    87631    87641    87643    94321
   96431    97651    98321    98543    98621    98641    98731   764321   865321   876431   975421
  986543   987541   987631  8764321  8765321  9754321  9875321 97654321 98764321 98765431

Unsorted, ie in the order in which they are generated:

There are 87 descending primes:
       2        3       31       41      421       43      431        5      521       53      541
    5431       61      631      641     6421      643     6521      653        7       71       73
    7321      743      751     7541    75431      761     7621    76421     7643   764321    76541
   76543      821       83     8431     8521      853     8543      863     8641    86531   865321
    8731     8741    87421     8753    87541     8761    87631    87641    87643   876431  8764321
 8765321      941     9421     9431    94321     9521      953     9631     9643    96431       97
     971     9721     9743   975421  9754321    97651 97654321      983    98321     9851    98543
   98621    98641   986543     9871    98731  9875321   987541   987631 98764321 98765431

Raku

Trivial variation of Ascending primes task.

<lang perl6>put (flat 2, 3, 5, 7, sort +*, gather (3..9).map: &recurse ).batch(10)».fmt("%8d").join: "\n";

sub recurse ($str) {

   .take for ($str X~ (1, 3, 7)).grep: { .is-prime && [>] .comb };
   recurse $str × 10 + $_ for 1 ..^ $str % 10;

}</lang>

Output:

       2        3        5        7       31       41       43       53       61       71
      73       83       97      421      431      521      541      631      641      643
     653      743      751      761      821      853      863      941      953      971
     983     5431     6421     6521     7321     7541     7621     7643     8431     8521
    8543     8641     8731     8741     8753     8761     9421     9431     9521     9631
    9643     9721     9743     9851     9871    75431    76421    76541    76543    86531
   87421    87541    87631    87641    87643    94321    96431    97651    98321    98543
   98621    98641    98731   764321   865321   876431   975421   986543   987541   987631
 8764321  8765321  9754321  9875321 97654321 98764321 98765431

Ring

This example is incorrect. Please fix the code and remove this message.

Details:
Many of the numbers shown do not have strictly descending digits, e.g. all the ones starting with 2 (except 2 itself).
Largest is much larger than 1000.

<lang ring> load "stdlibcore.ring"

limit = 1000 row = 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
   ok

next </lang> Output:
2 3 5 7 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