Palindromic primes

Palindromic primes 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 and show all palindromic primes   n,     where   n   <   1000

REXX

<lang rexx>/*REXX program finds and displays palindromic primes for all N < 500. */ 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= max(7, length( commas(hi) ) ) /*max width of a number in any column. */

                                   @pal= ' palindromic primes that are  < '    commas(hi)

if cols>0 then say ' index │'center(@pal, 1 + cols*(w+1) ) if cols>0 then say '───────┼'center("" , 1 + cols*(w+1), '─') pals= 0; idx= 1 /*define # of palindromic primes & idx.*/ $= /*a list of palindromic primes so far).*/

    do j=1  for #                               /*search for palindromic primes.       */
    if @.j\==reverse(@.j)  then iterate         /*Not a palindromic prime?  Then skip. */
    pals= pals + 1                              /*bump the number of palindromic primes*/
    if cols==0             then iterate         /*Build the list  (to be shown later)? */
    $= $ right( commas(@.j), w)                 /*add a palindromic prime ──►  $  list.*/
    if pals//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), '─') say say 'Found ' commas(pals) @pal 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: !.= 0; hprime= copies(9, length(hi) ) /*placeholders for primes (semaphores).*/

     @.1=2;  @.2=3;  @.3=5;  @.4=7;  @.5=11     /*define some low primes.              */
     !.2=1;  !.3=1;  !.5=1;  !.7=1;  !.11=1     /*   "     "   "    "     flags.       */
                     #=5;     s.#= @.# **2      /*number of primes so far;     prime². */
                                                /* [↓]  generate more  primes  ≤  high.*/
       do j=@.#+2  by 2  to hprime              /*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?             */
                            if j// 7==0  then iterate  /*"     "      " 7?             */
                                                /* [↑]  the above  3  lines saves time.*/
              do k=5  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;   !.j= 1 /*bump # of Ps; assign next P;  P²; P# */
       end          /*j*/;   return</lang>

output   when using the default inputs:

 index │                      palindromic primes that are  <  1,000
───────┼─────────────────────────────────────────────────────────────────────────────────
   1   │       2       3       5       7      11     101     131     151     181     191
  11   │     313     353     373     383     727     757     787     797     919     929
───────┴─────────────────────────────────────────────────────────────────────────────────

Found  20  palindromic primes that are  <  1,000

output   when using the input of:     100000

 index │                     palindromic primes that are  <  100,000
───────┼─────────────────────────────────────────────────────────────────────────────────
   1   │       2       3       5       7      11     101     131     151     181     191
  11   │     313     353     373     383     727     757     787     797     919     929
  21   │  10,301  10,501  10,601  11,311  11,411  12,421  12,721  12,821  13,331  13,831
  31   │  13,931  14,341  14,741  15,451  15,551  16,061  16,361  16,561  16,661  17,471
  41   │  17,971  18,181  18,481  19,391  19,891  19,991  30,103  30,203  30,403  30,703
  51   │  30,803  31,013  31,513  32,323  32,423  33,533  34,543  34,843  35,053  35,153
  61   │  35,353  35,753  36,263  36,563  37,273  37,573  38,083  38,183  38,783  39,293
  71   │  70,207  70,507  70,607  71,317  71,917  72,227  72,727  73,037  73,237  73,637
  81   │  74,047  74,747  75,557  76,367  76,667  77,377  77,477  77,977  78,487  78,787
  91   │  78,887  79,397  79,697  79,997  90,709  91,019  93,139  93,239  93,739  94,049
  101  │  94,349  94,649  94,849  94,949  95,959  96,269  96,469  96,769  97,379  97,579
  111  │  97,879  98,389  98,689
───────┴─────────────────────────────────────────────────────────────────────────────────

Found  113  palindromic primes that are  <  100,000

Ring

<lang ring> load "stdlib.ring"

decimals(0) see "working..." + nl see "Palindromic primes are:" + nl

row = 0 limit = 1000

for n = 1 to limit

   strn = string(n)
   if ispalindrome(strn) and isprime(n)
      row = row + 1
      see "" + n + " "
      if row%5 = 0
         see nl
      ok
   ok

next

see "Found " + row + " palindromic primes" + nl see "done..." + nl </lang>

Output:

working...
Palindromic primes are:
2 3 5 7 11 
101 131 151 181 191 
313 353 373 383 727 
757 787 797 919 929 
Found 20 palindromic primes
done...