Erdős-primes

Erdős-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.

Definitions

In mathematics, Erdős-primes are prime numbers which sum of digits are also primes.

Task

Write a program to determine (and show here) all Erdős-primes whose elements are less than 500.

Optionally, show the number of Erdős-primes.

REXX

<lang rexx>/*REXX program counts and shows the number of Erdős primes under a specified number N. */ parse arg n cols . /*get optional number of primes to find*/ if n== | n=="," then n= 500 /*Not specified? Then assume default.*/ if cols== | cols=="," then cols= 10 /* " " " " " .*/ Ocols= cols; cols= abs(cols) /*Use the absolute value of cols. */ call genP n /*generate all primes under N. */ primes= 0 /*initialize the number of Erdős primes*/ $= /*a list of Erdős primes (so far). */

      do j=1  until j>=n; if \!.j  then iterate /*Is  J  not a prime?  Then skip it.   */
      _= sumDigs(j);      if \!._  then iterate /*Is sum of J's digs a prime? No, skip.*/
      primes= primes + 1                        /*bump the count of Erdős primes.      */
      if Ocols<1           then iterate         /*Build the list  (to be shown later)? */
      $= $  right(j, w)                         /*add the Erdős prime to the  $  list. */
      if primes//cols\==0  then iterate         /*have we populated a line of output?  */
      say substr($, 2);    $=                   /*display what we have so far  (cols). */
      end   /*j*/

if $\== then say substr($, 2) /*possible display some residual output*/ say say 'found ' primes " Erdős primes < " n exit 0 /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ sumDigs: parse arg x 1 s 2; do k=2 for length(x)-1; s= s + substr(x,k,1); end; return s /*──────────────────────────────────────────────────────────────────────────────────────*/ genP: parse arg n; @.=.; @.1=2; @.2=3; @.3=5; @.4=7; @.5=11; @.6=13; @.7=17; #= 7

     w= length(n);  !.=0; !.2=1;  !.3=1;  !.5=1;  !.7=1;  !.11=1;  !.13=1;  !.17=1
           do j=@.7+2  by 2  while j<n          /*continue on with the next odd prime. */
           parse var  j    -1  _              /*obtain the last digit of the  J  var.*/
           if _      ==5  then iterate          /*is this integer a multiple of five?  */
           if j // 3 ==0  then iterate          /* "   "     "    "     "     " three? */
                                                /* [↓]  divide by the primes.   ___    */
                 do k=4  to #  while  k*k<=j    /*divide  J  by other primes ≤ √ J     */
                 if j//@.k == 0  then iterate j /*÷ by prev. prime?  ¬prime     ___    */
                 end   /*k*/                    /* [↑]   only divide up to     √ J     */
           #= # + 1;          @.#= j;    !.j= 1 /*bump prime count; assign prime & flag*/
           end   /*j*/
    return</lang>

output   when using the default inputs:

  2   3   5   7  11  23  29  41  43  47
 61  67  83  89 101 113 131 137 139 151
157 173 179 191 193 197 199 223 227 229
241 263 269 281 283 311 313 317 331 337
353 359 373 379 397 401 409 421 443 449
461 463 467 487

found  54  Erdős primes  <  500

Ring

<lang ring> load "stdlib.ring"

see "working..." + nl see "Erdős-primes are:" + nl

row = 0 limit = 500

for n = 1 to limit

   num = 0
   if isprime(n) 
      strn = string(n)
      for m = 1 to len(strn)
          num = num + number(strn[m])
      next
      if isprime(num)
         row = row + 1
         see "" + n + " "
         if row%10 = 0
            see nl
         ok
      ok
   ok

next

see nl + "found " + row + " Erdös-primes." + nl see "done..." + nl </lang>

Output:

working...
Erdős-primes are:
2 3 5 7 11 23 29 41 43 47 
61 67 83 89 101 113 131 137 139 151 
157 173 179 191 193 197 199 223 227 229 
241 263 269 281 283 311 313 317 331 337 
353 359 373 379 397 401 409 421 443 449 
461 463 467 487 
found 54 Erdös-primes.
done...