Find prime n for that reversed n is also prime

Find prime n for that reversed n is also prime 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 prime   n     for   0 < n < 500     which are also primes when the (decimal) digits are reversed.

ALGOL W

begin % find some primes whose digits reversed is also prime %
    % sets p( 1 :: n ) to a sieve of primes up to n %
    procedure Eratosthenes ( logical array p( * ) ; integer value n ) ;
    begin
        p( 1 ) := false; p( 2 ) := true;
        for i := 3 step 2 until n do p( i ) := true;
        for i := 4 step 2 until n do p( i ) := false;
        for i := 3 step 2 until truncate( sqrt( n ) ) do begin
            integer ii; ii := i + i;
            if p( i ) then for pr := i * i step ii until n do p( pr ) := false
        end for_i ;
    end Eratosthenes ;
    integer MAX_NUMBER, maxPrime;
    MAX_NUMBER := 500;
    % approximate the largest prime we need to consider ( 10 ^ number of digits in MAX_NUMBER ) %
    begin
        integer v;
        v        := MAX_NUMBER;
        maxPrime := 1;
        while v > 0 do begin
            v := v div 10;
            maxPrime := maxPrime * 10
        end while_v_gt_0
    end;
    begin
        logical array prime( 1 :: maxPrime);
        integer       pCount;
        % sieve the primes to maxPrime %
        Eratosthenes( prime, maxPrime );
        % find the primes that are reversable %
        pCount := 0;
        for i := 1 until MAX_NUMBER - 1 do begin
            if prime( i ) then begin
                integer pReversed, v;
                v         := i;
                pReversed := 0;
                while v > 0 do begin
                    pReversed := ( pReversed * 10 ) + v rem 10;
                    v         := v div 10
                end while_v_gt_0 ;
                if prime( pReversed ) then begin
                    writeon( i_w := 4, s_w := 0, " ", i );
                    pCount := pCount + 1;
                    if pCount rem 20 = 0 then write()
                end if_prime_pReversed
            end if_prime_i
        end for_i ;
        write( i_w := 1, s_w := 0, "Found ", pCount, " reversable primes below ", MAX_NUMBER )
    end
end.

Output:

    2    3    5    7   11   13   17   31   37   71   73   79   97  101  107  113  131  149  151  157
  167  179  181  191  199  311  313  337  347  353  359  373  383  389
Found 34 reversable primes below 500

AWK

 
# syntax: GAWK -f FIND_PRIME_N_FOR_THAT_REVERSED_N_IS_ALSO_PRIME.AWK
BEGIN {
    start = 1
    stop = 500
    for (i=start; i<=stop; i++) {
      if (is_prime(i) && is_prime(revstr(i,length(i)))) {
        printf("%3d%1s",i,++count%10?"":"\n")
      }
    }
    printf("\nReversible primes %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)
}
function revstr(str,start) {
    if (start == 0) {
      return("")
    }
    return( substr(str,start,1) revstr(str,start-1) )
}
 

Output:

  2   3   5   7  11  13  17  31  37  71
 73  79  97 101 107 113 131 149 151 157
167 179 181 191 199 311 313 337 347 353
359 373 383 389
Reversible primes 1-500: 34

Delphi

Library: System.SysUtils

Library: PrimTrial

Translation of: Ring

 
program Find_prime_n_for_that_reversed_n_is_also_prime;
 
{$APPTYPE CONSOLE}
 
uses
  System.SysUtils,
  PrimTrial;
 
function Reverse(s: string): string;
var
  i: Integer;
begin
  Result := '';
  if Length(s) < 2 then
    exit(s);
  for i := Length(s) downto 1 do
    Result := Result + s[i];
end;
 
begin
  writeln('working...'#10);
  var row := 0;
  var count := 0;
  var limit := 500;
 
  for var n := 1 to limit - 1 do
  begin
    if not isPrime(n) then
      Continue;
 
    var val := n.ToString;
    var valr := reverse(val);
    var nr := valr.ToInteger;
 
    if not isPrime(nr) then
      Continue;
 
    write(n: 4);
 
    inc(row);
    inc(count);
    if row mod 10 = 0 then
      writeln;
  end;
  writeln(#10#10, 'found ', count, ' primes');
  Writeln('done...');
  readln;
end.

Output:

working...

   2   3   5   7  11  13  17  31  37  71
  73  79  97 101 107 113 131 149 151 157
 167 179 181 191 199 311 313 337 347 353
 359 373 383 389

found 34 primes
done...

F#

This task uses Extensible Prime Generator (F#)

 
// Reversible Primes. Nigel Galloway: March 22nd., 2021
let emirp2=let rec fN g=function |0->g |n->fN(g*10+n%10)(n/10) in primes32()|>Seq.filter(fN 0>>isPrime)
emirp2|>Seq.takeWhile((>)500)|>Seq.iter(printf "%d "); printfn ""
 

Output:

2 3 5 7 11 13 17 31 37 71 73 79 97 101 107 113 131 149 151 157 167 179 181 191 199 311 313 337 347 353 359 373 383 389

Factor

Works with: Factor version 0.99 2021-02-05

USING: formatting grouping io kernel math math.primes sequences ;
 
: reverse-digits ( 123 -- 321 )
    0 swap [ 10 /mod rot 10 * + swap ] until-zero ;
 
499 primes-upto [ reverse-digits prime? ] filter
dup length "Found %d reverse primes < 500.\n\n" printf
10 group [ [ "%4d" printf ] each nl ] each nl

Output:

Found 34 reverse primes < 500.

   2   3   5   7  11  13  17  31  37  71
  73  79  97 101 107 113 131 149 151 157
 167 179 181 191 199 311 313 337 347 353
 359 373 383 389

FreeBASIC

Use one of the primality testing algorithms as an include as I can't be bothered putting these in all the time.

#include "isprime.bas"
 
function isbackprime( byval n as integer ) as boolean
    if not isprime(n) then return false
    dim as integer m = 0
    while n
        m *= 10
        m += n mod 10
        n \= 10
    wend
    return isprime(m)
end function
 
for n as uinteger = 2 to 499
    if isbackprime(n) then print n;" ";
next n
print

Output:

2 3 5 7 11 13 17 31 37 71 73 79 97 101 107 113 131 149 151 157 167 179 181 191 199 311 313 337 347 353 359 373 383 389

Go

package main
 
import "fmt"
 
func sieve(limit int) []bool {
    limit++
    // True denotes composite, false denotes prime.
    c := make([]bool, limit) // all false by default
    c[0] = true
    c[1] = true
    for i := 4; i < limit; i += 2 {
        c[i] = true
    }
    p := 3 // Start from 3.
    for {
        p2 := p * p
        if p2 >= limit {
            break
        }
        for i := p2; i < limit; i += 2 * p {
            c[i] = true
        }
        for {
            p += 2
            if !c[p] {
                break
            }
        }
    }
    return c
}
 
func reversed(n int) int {
    rev := 0
    for n > 0 {
        rev = rev*10 + n%10
        n /= 10
    }
    return rev
}
 
func main() {
    c := sieve(999)
    reversedPrimes := []int{2}
    for i := 3; i < 500; i += 2 {
        if !c[i] && !c[reversed(i)] {
            reversedPrimes = append(reversedPrimes, i)
        }
    }
    fmt.Println("Primes under 500 which are also primes when the digits are reversed:")
    for i, p := range reversedPrimes {
        fmt.Printf("%5d", p)
        if (i+1) % 10 == 0 {
            fmt.Println()
        }
    }
    fmt.Printf("\n\n%d such primes found.\n", len(reversedPrimes))
}

Output:

Primes under 500 which are also primes when the digits are reversed:
    2    3    5    7   11   13   17   31   37   71
   73   79   97  101  107  113  131  149  151  157
  167  179  181  191  199  311  313  337  347  353
  359  373  383  389

34 such primes found.

Haskell

import Data.List (intercalate, transpose)
import Data.List.Split (chunksOf)
import Data.Numbers.Primes (isPrime, primes)
import Text.Printf (printf)
 
------------------------ PREDICATE -----------------------
 
p :: Int -> Bool
p n = isPrime (read (reverse $ show n) :: Int)
 
--------------------------- TEST -------------------------
main :: IO ()
main =
  mapM_
    putStrLn
    [ "Reversible primes below 500:",
      (table " " . chunksOf 10 . fmap show) $
        takeWhile (< 500) (filter p primes)
    ]
 
------------------------ FORMATTING ----------------------
 
table :: String -> [[String]] -> String
table gap rows =
  let widths =
        maximum . fmap length
          <$> transpose rows
   in unlines $
        fmap
          ( intercalate gap
              . zipWith
                ( printf
                    . flip intercalate ["%", "s"]
                    . show
                )
                widths
          )
          rows

Output:

Reversible primes below 500:
  2   3   5   7  11  13  17  31  37  71
 73  79  97 101 107 113 131 149 151 157
167 179 181 191 199 311 313 337 347 353
359 373 383 389

Julia

using Primes
 
let
    pmask, pcount = primesmask(1, 994), 0
    isreversibleprime(n) = pmask[n] && pmask[evalpoly(10, reverse(digits(n)))]
 
    println("Reversible primes between 0 and 500:")
    for n in 1:499
        if isreversibleprime(n)
            pcount += 1
            print(rpad(n, 4), pcount % 17 == 0 ? "\n" : "")
        end
    end
    println("Total found: $pcount")
end
 

Output:

Reversible primes between 0 and 500:
2   3   5   7   11  13  17  31  37  71  73  79  97  101 107 113 131 
149 151 157 167 179 181 191 199 311 313 337 347 353 359 373 383 389
Total found: 34

Perl

Library: ntheory

use strict;
use warnings;
use List::Util 'max';
use ntheory 'is_prime';
 
sub pp {
    my $format = ('%' . (my $cw = 1+length max @_) . 'd') x @_;
    my $width  = ".{@{[$cw * int 60/$cw]}}";
    (sprintf($format, @_)) =~ s/($width)/$1\n/gr;
}
 
my($limit, @rp) = 500;
is_prime($_) and is_prime(reverse $_) and push @rp, $_ for 1..$limit;
print @rp . " reversible primes < $limit:\n" . pp(@rp);

Output:

34 reversible primes < 500:
   2   3   5   7  11  13  17  31  37  71  73  79  97 101 107
 113 131 149 151 157 167 179 181 191 199 311 313 337 347 353
 359 373 383 389

Phix

function rp(integer p) return is_prime(to_integer(reverse(sprint(p)))) end function
procedure test(sequence args)
    {integer n, string fmt} = args
    sequence res = apply(true,sprintf,{{"%3d"},filter(get_primes_le(n),rp)})
    string r = sprintf(fmt,{join_by(res,1,ceil(length(res)/2)," ")})
    printf(1,"%,d reverse primes < %,d found%s\n",{length(res),n,r})
end procedure
papply({{500,":\n%s"},{1000,":\n%s"},{10000,"."},{10_000_000,"."}},test)

Output:

34 reverse primes < 500 found:
  2   3   5   7  11  13  17  31  37  71  73  79  97 101 107 113 131
149 151 157 167 179 181 191 199 311 313 337 347 353 359 373 383 389

56 reverse primes < 1,000 found:
  2   3   5   7  11  13  17  31  37  71  73  79  97 101 107 113 131 149 151 157 167 179 181 191 199 311 313 337
347 353 359 373 383 389 701 709 727 733 739 743 751 757 761 769 787 797 907 919 929 937 941 953 967 971 983 991

260 reverse primes < 10,000 found.
82,439 reverse primes < 10,000,000 found.

Raku

unit sub MAIN ($limit = 500);
say "{+$_} reversible primes < $limit:\n{$_».fmt("%" ~ $limit.chars ~ "d").batch(10).join("\n")}",
    with ^$limit .grep: { .is-prime and .flip.is-prime }

Output:

34 reversible primes < 500:
  2   3   5   7  11  13  17  31  37  71
 73  79  97 101 107 113 131 149 151 157
167 179 181 191 199 311 313 337 347 353
359 373 383 389

REXX

/*REXX program counts/displays the number of reversed 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          /* "      "          "     "       "   */
call genP copies(9, length(n) )                  /*generate all primes under  N.        */
w= 10                                            /*width of a number in any column.     */
if cols>0  then say ' index │'center(" reversed primes that are  < "  n,  1 + cols*(w+1) )
if cols>0  then say '───────┼'center(""                           ,  1 + cols*(w+1),  '─')
Rprimes= 0;                idx= 1                /*initialize # of additive primes & idx*/
$=                                               /*a list of additive primes  (so far). */
       do j=2  until j>=n; if \!.j  then iterate /*Is  J  not a prime? No, then skip it.*/
       _= reverse(j);      if \!._  then iterate /*is sum of J's digs a prime? No, skip.*/
       Rprimes= Rprimes + 1                      /*bump the count of additive primes.   */
       if cols<1             then iterate        /*Build the list  (to be shown later)? */
       $= $  right( commas(j), w)                /*add the additive prime to the $ list.*/
       if Rprimes//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(Rprimes)       " reversed primes  < "       commas(n)
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: parse arg h;   @.=.; @.1=2;  @.2=3;  @.3=5;  @.4=7;  @.5=11;  @.6=13;  @.7=17;  #= 7
      w= length(h);  !.=0; !.2=1;  !.3=1;  !.5=1;  !.7=1;  !.11=1;  !.13=1;  !.17=1
            do [email protected].7+2  by 2  while j<h          /*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

output   when using the default inputs:

 index │                                        reversed primes that are  <  500
───────┼───────────────────────────────────────────────────────────────────────────────────────────────────────────────
   1   │          2          3          5          7         11         13         17         31         37         71
  11   │         73         79         97        101        107        113        131        149        151        157
  21   │        167        179        181        191        199        311        313        337        347        353
  31   │        359        373        383        389

found  34  reversed primes  <  500

output   when using the inputs:     10000   0

found  260  reversed primes  <  10,000

Ring

 
load "stdlib.ring"
 
see "working..." + nl
 
row = 0
num = 0
limit = 500
 
for n = 1 to limit
    strm = ""
    strn = string(n)
    for m = len(strn) to 1 step -1
        strm = strm + strn[m]
    next
    strnum = number(strm)
    if isprime(n) and isprime(strnum)
       num = num + 1
       row = row + 1
       see "" + n + " "
       if row%10 = 0
          see nl
       ok
     ok       
next
 
see nl + "found " + num + " primes" + nl
see "done..." + nl
 

Output:

working...
2 3 5 7 11 13 17 31 37 71 
73 79 97 101 107 113 131 149 151 157 
167 179 181 191 199 311 313 337 347 353 
359 373 383 389 
found 34 primes
done...

Wren

Library: Wren-math

Library: Wren-fmt

Library: Wren-seq

import "/math" for Int
import "/fmt" for Fmt
import "/seq" for Lst
 
var reversed = Fn.new { |n|
    var rev = 0
    while (n > 0) {
        rev = rev * 10 + n % 10
        n = (n/10).floor
    }
    return rev
}
 
var primes = Int.primeSieve(499)
var reversedPrimes = []
for (p in primes) {
    if (Int.isPrime(reversed.call(p))) reversedPrimes.add(p)
}
System.print("Primes under 500 which are also primes when the digits are reversed:")
for (chunk in Lst.chunks(reversedPrimes, 17)) Fmt.print("$3d", chunk)
System.print("\n%(reversedPrimes.count) such primes found.")

Output:

Primes under 500 which are also primes when the digits are reversed:
  2   3   5   7  11  13  17  31  37  71  73  79  97 101 107 113 131
149 151 157 167 179 181 191 199 311 313 337 347 353 359 373 383 389

34 such primes found.