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

ALGOL 68

Generates the palindrmic 3 digit numbers and uses the observations that all 1 digit primes are palindromic and that for 2 digit numbers, only multiples of 11 are palindromic and hence 11 is the only two digit palindromic prime.

Library: ALGOL 68-primes

<lang algol68>BEGIN # find primes that are palendromic in base 10 #

   INT max prime = 999;
   # sieve the primes to max prime #
   PR read "primes.incl.a68" PR
   []BOOL prime = PRIMESIEVE max prime;
   # print the palendromic primes in the base 10 #
   # all 1 digit primes are palindromic #
   FOR n TO 9 DO IF prime[ n ] THEN print( ( " ", whole( n, 0 ) ) ) FI OD;
   # the only palindromic 2 digit numbers are multiples of 11 #
   # so 11 is the only possible 2 digit palindromic prime #
   IF prime[ 11 ] THEN print( ( " 11" ) ) FI;
   # three digit numbers, the first and last digits must be odd #
   # and cannot be 5 (as the number would be divisible by 5) #
   FOR fl BY 2 TO 9 DO
       IF fl /= 5 THEN
           FOR m FROM 0 TO 9 DO
               INT n = ( ( ( fl * 10 ) + m ) * 10 ) + fl;
               IF prime[ n ] THEN
                   # have a palindromic prime #
                   print( ( " ", whole( n, 0 ) ) )
               FI
           OD
       FI
   OD;
   print( ( newline ) )

END</lang>

Output:

 2 3 5 7 11 101 131 151 181 191 313 353 373 383 727 757 787 797 919 929

Arturo

<lang rebol>loop split.every: 10 select 2..1000 'x [

   and? prime? x
        x = to :integer reverse to :string x

] 'a -> print map a => [pad to :string & 4]</lang>

Output:

   2    3    5    7   11  101  131  151  181  191 
 313  353  373  383  727  757  787  797  919  929

AWK

<lang AWK>

1. syntax: GAWK -f PALINDROMIC_PRIMES.AWK

BEGIN {

   start = 1
   stop = 999
   for (i=start; i<=stop; i++) {
     if (is_prime(i) && reverse(i) == i) {
       printf("%d ",i)
       count++
     }
   }
   printf("\nPalindromic 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 reverse(str, i,rts) {

   for (i=length(str); i>=1; i--) {
     rts = rts substr(str,i,1)
   }
   return(rts)

} </lang>

Output:

2 3 5 7 11 101 131 151 181 191 313 353 373 383 727 757 787 797 919 929
Palindromic primes 1-999: 20

Factor

Simple

A simple solution that suffices for the task:

Works with: Factor version 0.99 2021-02-05

<lang factor>USING: kernel math.primes present prettyprint sequences ;

1000 primes-upto [ present dup reverse = ] filter stack.</lang>

Output:

2
3
5
7
11
101
131
151
181
191
313
353
373
383
727
757
787
797
919
929

Fast

A much more efficient solution that generates palindromic numbers directly and filters primes from them:

Works with: Factor version 0.99 2021-02-05

<lang factor>USING: io kernel lists lists.lazy math math.functions math.primes math.ranges prettyprint sequences tools.memory.private ;

! Create a palindrome from its base natural number.

create-palindrome ( n odd? -- m )

   dupd [ 10 /i ] when swap [ over 0 > ]
   [ 10 * [ 10 /mod ] [ + ] bi* ] while nip ;

! Create an ordered infinite lazy list of palindromic numbers.

lpalindromes ( -- l )

   0 lfrom [
       10 swap ^ dup 10 * [a,b)
       [ [ t create-palindrome ] map ]
       [ [ f create-palindrome ] map ] bi
       [ sequence>list ] bi@ lappend
   ] lmap-lazy lconcat ;

lpalindrome-primes ( -- list )

   lpalindromes [ prime? ] lfilter ;

"10,000th palindromic prime:" print 9999 lpalindrome-primes lnth commas print nl

"Palindromic primes less than 1,000:" print lpalindrome-primes [ 1000 < ] lwhile [ . ] leach</lang>

Output:

10,000th palindromic prime:
13,649,694,631

Palindromic primes less than 1,000:
2
3
5
7
11
101
131
151
181
191
313
353
373
383
727
757
787
797
919
929

FreeBASIC

<lang freebasic>#include "isprime.bas"

function is_pal( s as string ) as boolean

   dim as integer i, n = len(s)
   for i = 1 to n\2
       if mid(s,i,1)<>mid(s,n-i+1,1) then return false
   next i
   return true

end function

for i as uinteger = 2 to 999

   if is_pal( str(i) ) andalso isprime(i) then  print i;" ";

next i : print</lang>

Output:

2 3 5 7 11 101 131 151 181 191 313 353 373 383 727 757 787 797 919 929

Go

Translation of: Wren

Library: Go-rcu

<lang go>package main

import (

   "fmt"
   "rcu"

)

func reversed(n int) int {

   rev := 0
   for n > 0 {
       rev = rev*10 + n%10
       n /= 10
   }
   return rev

}

func main() {

   primes := rcu.Primes(99999)
   var pals []int
   for _, p := range primes {
       if p == reversed(p) {
           pals = append(pals, p)
       }
   }
   fmt.Println("Palindromic primes under 1,000:")
   var smallPals, bigPals []int
   for _, p := range pals {
       if p < 1000 {
           smallPals = append(smallPals, p)
       } else {
           bigPals = append(bigPals, p)
       }
   }
   rcu.PrintTable(smallPals, 10, 3, false)
   fmt.Println()
   fmt.Println(len(smallPals), "such primes found.")

   fmt.Println("\nAdditional palindromic primes under 100,000:")
   rcu.PrintTable(bigPals, 10, 6, true)
   fmt.Println()
   fmt.Println(len(bigPals), "such primes found,", len(pals), "in all.")

}</lang>

Output:

Same as Wren entry.

Haskell

<lang haskell>import Data.Numbers.Primes

palindromicPrimes :: [Integer] palindromicPrimes =

 filter (((==) <*> reverse) . show) primes

main :: IO () main =

 mapM_ print $
   takeWhile
     (1000 >)
     palindromicPrimes</lang>

Output:

2
3
5
7
11
101
131
151
181
191
313
353
373
383
727
757
787
797
919
929

jq

Works with: jq

Works with gojq, the Go implementation of jq

In this entry, we define both a naive generate-and-test generator of the palindromic primes, and a more sophisticated one that is well-suited for generating very large numbers of such primes, as illustrated by counting the number less than 10^10.

For a suitable implementation of `is_prime` as used here, see Erdős-primes#jq.

Preliminaries <lang jq>def count(s): reduce s as $x (null; .+1);

def emit_until(cond; stream): label $out | stream | if cond then break $out else . end;</lang> Naive version <lang jq> def primes:

 2, (range(3;infinite;2) | select(is_prime));

def palindromic_primes_slowly:

 primes | select( tostring|explode | (. == reverse));

</lang> Less naive version <lang jq># Output: an unbounded stream of palindromic primes def palindromic_primes:

 # Output: a naively constructed stream of palindromic strings of length >= 2
 def palindromic_candidates:
   def rev: # reverse a string
     explode|reverse|implode;
   def unconstrained($length):
     if $length==1 then range(0;10) | tostring
     else (range(0;10)|tostring)
     | . + unconstrained($length -1 )
     end;
   def middle($length):  # $length > 0
     if $length==1 then range(0;10) | tostring
     elif $length % 2 == 1
     then (($length -1) / 2) as $len
     | unconstrained($len) as $left
     | (range(0;10) | tostring) as $mid
     | $left + $mid + ($left|rev)
     else ($length / 2) as $len
     | unconstrained($len) as $left
     | $left + ($left|rev)
     end;
 
 # palindromes with an even number of digits are divisible by 11

   range(1;infinite;2) as $mid
   | ("1", "3", "7", "9") as $start
   | $start + middle($mid) + $start ;
 
 2, 3, 5, 7, 11,
 (palindromic_candidates | tonumber | select(is_prime));</lang>

Demonstrations <lang jq>"Palindromic primes < 1000:", emit_until(. >= 1000; palindromic_primes),

((range(5;11) | pow(10;.)) as $n

| "\nNumber of palindromic primes <= \($n): \(count(emit_until(. >= $n; palindromic_primes)))" )</lang>

Output:

Palindromic primes <= 1000:
2
3
5
7
11
101
131
151
181
191
313
353
373
383
727
757
787
797
919
929

Number of palindromic primes <= 100000: 113

Number of palindromic primes <= 1000000: 113

Number of palindromic primes <= 10000000: 781

Number of palindromic primes <= 100000000: 781

Number of palindromic primes <= 1000000000: 5953

Number of palindromic primes <= 10000000000: 5953

Julia

Generator method. <lang julia>using Primes

parray = [2, 3, 5, 7, 9, 11]

results = vcat(parray, filter(isprime, [100j + 10i + j for i in 0:9, j in 1:9]))

println(results)

</lang>

Output:

[2, 3, 5, 7, 9, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929]

Mathematica/Wolfram Language

<lang Mathematica>Select[Range[999], PrimeQ[#] \[And] PalindromeQ[#] &]</lang>

Output:

{2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929}

Nim

<lang Nim>import strutils

const N = 999

func isPrime(n: Positive): bool =

 if (n and 1) == 0: return n == 2
 var m = 3
 while m * m <= n:
   if n mod m == 0: return false
   inc m, 2
 result = true

func reversed(n: Positive): int =

 var n = n.int
 while n != 0:
   result = 10 * result + n mod 10
   n = n div 10

func isPalindromic(n: Positive): bool =

 n == reversed(n)

var result: seq[int] for n in 2..N:

 if n.isPrime and n.isPalindromic:
   result.add n

for i, n in result:

 stdout.write ($n).align(3)
 stdout.write if (i + 1) mod 10 == 0: '\n' else: ' '</lang>

Output:

  2   3   5   7  11 101 131 151 181 191
313 353 373 383 727 757 787 797 919 929

Perl

<lang Perl>#!/usr/bin/perl

use strict; # https://rosettacode.org/wiki/Palindromic_primes use warnings;

$_ == reverse and (1 x $_ ) !~ /^(11+)\1+$/ and print "$_\n" for 2 .. 1e3;</lang>

Output:

2 3 5 7 11 101 131 151 181 191 313 353 373 383 727 757 787 797 919 929

Phix

filter primes for palindromicness

function palindrome(string s) return s=reverse(s) end function
for l=3 to 5 by 2 do
    integer limit = power(10,l) -- 1000 then 100000
    sequence res = get_primes_le(limit)
    res = apply(true,sprintf,{{"%d"},res})
    res = filter(res,palindrome)
    string s = join(shorten(res,"",5))
    printf(1,"found %d < %,d: %s\n",{length(res),limit,s})
end for

Output:

found 20 < 1,000: 2 3 5 7 11 ... 757 787 797 919 929
found 113 < 100,000: 2 3 5 7 11 ... 97379 97579 97879 98389 98689

filter palindromes for primality

sequence r = {}
for l=2 to 3 do
    for i=1 to power(10,l) do
        string s = sprintf("%d",i)
        integer t = to_number(s&reverse(s[1..$-1])),
                u = to_number(s&reverse(s))
        if is_prime(t) then r &= t end if
        if is_prime(u) then r &= u end if
    end for
    r = unique(r)
    string s = join(shorten(apply(true,sprintf,{{"%d"},r}),"",5))
    printf(1,"found %d < %,d: %s\n",{length(r),power(10,l*2-1),s})
end for

Same output. Didn't actually test if this way was any faster, but expect it would be.

Python

A non-finite generator of palindromic primes – one of many approaches to solving this problem in Python. <lang python>Palindromic primes

from itertools import takewhile

1. palindromicPrimes :: Generator [Int]

def palindromicPrimes():

   An infinite stream of palindromic primes
   def p(n):
       s = str(n)
       return s == s[::-1]
   return (n for n in primes() if p(n))

1. ------------------------- TEST -------------------------

def main():

   Palindromic primes below 1000
   print('\n'.join(
       str(x) for x in takewhile(
           lambda n: 1000 > n,
           palindromicPrimes()
       )
   ))

1. ----------------------- GENERIC ------------------------

1. primes :: [Int]

def primes():

    Non finite sequence of prime numbers.
   
   n = 2
   dct = {}
   while True:
       if n in dct:
           for p in dct[n]:
               dct.setdefault(n + p, []).append(p)
           del dct[n]
       else:
           yield n
           dct[n * n] = [n]
       n = 1 + n

1. MAIN ---

if __name__ == '__main__':

   main()

</lang>

Output:

2
3
5
7
11
101
131
151
181
191
313
353
373
383
727
757
787
797
919
929

Raku

<lang perl6>say "{+$_} matching numbers:\n{.batch(10)».fmt('%3d').join: "\n"}"

   given (^1000).grep: { .is-prime and $_ eq .flip };</lang>

Output:

20 matching numbers:
  2   3   5   7  11 101 131 151 181 191
313 353 373 383 727 757 787 797 919 929

REXX

<lang rexx>/*REXX program finds and displays palindromic primes in base ten for all N < 1,000.*/ 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(8, length( commas(hi) ) ) /*max width of a number in any column. */

                     title= ' palindromic primes in base ten that are  < '    commas(hi)

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

    do j=1  for hi;  if \!.j  then iterate      /*Is this number not prime?  Then skip.*/     /* ◄■■■■■■■■ a filter. */
    if j\==reverse(j)         then iterate      /*Not a palindromic prime?     "    "  */     /* ◄■■■■■■■■ a filter. */
    finds= finds + 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 finds//cols\==0        then iterate      /*have we populated a line of output?  */
    say center(idx, 7)'|'  substr($, 2);   $=   /*display what we have so for  (cols). */
    idx= idx + cols                             /*bump the  index  count for the output*/
    end   /*j*/

if $\== then say center(idx, 7)'|' substr($, 2) /*possibly display residual output.*/ if cols>0 then say '───────┴'center("", 1 + cols*(w+1), '─') say say 'Found ' commas(finds) title 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; hip= max(hi, 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;     sq.#= @.# **2     /*number of primes so far;     prime². */
                                                /* [↓]  generate more  primes  ≤  high.*/
       do j=@.#+2  by 2  to hip                 /*find odd primes from here on.        */
       parse var j  -1 _;       if    _==5  then iterate  /*J ÷ by 5?  (right digit).*/
       if j//3==0  then iterate;  if j//7==0  then iterate  /*" "  " 3?     J ÷ by 7?  */
              do k=5  while sq.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;   sq.#= 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 in base ten 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 in base ten that are  <  1,000

output   when using the input of:     100000

 index │                    palindromic primes in base ten 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 in base ten that are  <  100,000

Ring

<lang ring> load "stdlib.ring"

see "working..." + nl see "Palindromic primes are:" + nl row = 0 limit1 = 1000 limit2 = 100000

palindromicPrimes(limit1)

see "Found " + row + " palindromic primes" + nl + nl see "palindromic primes that are < 100,000" + nl

palindromicPrimes(limit2)

see nl + "Found " + row + " palindromic primes that are < 100,000" + nl see "done..." + nl

func palindromicPrimes(limit)

    row = 0 
    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

</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

palindromic primes that are  <  100,000
2 3 5 7 11 
101 131 151 181 191 
313 353 373 383 727 
757 787 797 919 929 
10301 10501 10601 11311 11411 
12421 12721 12821 13331 13831 
13931 14341 14741 15451 15551 
16061 16361 16561 16661 17471 
17971 18181 18481 19391 19891 
19991 30103 30203 30403 30703 
30803 31013 31513 32323 32423 
33533 34543 34843 35053 35153 
35353 35753 36263 36563 37273 
37573 38083 38183 38783 39293 
70207 70507 70607 71317 71917 
72227 72727 73037 73237 73637 
74047 74747 75557 76367 76667 
77377 77477 77977 78487 78787 
78887 79397 79697 79997 90709 
91019 93139 93239 93739 94049 
94349 94649 94849 94949 95959 
96269 96469 96769 97379 97579 
97879 98389 98689 
Found 113 palindromic primes that are < 100,000
done...

Rust

This includes a solution for the similar task Palindromic primes in base 16. <lang rust>// [dependencies] // primal = "0.3" // radix_fmt = "1.0"

fn reverse(base: u64, mut n: u64) -> u64 {

   let mut rev = 0;
   while n > 0 {
       rev = rev * base + n % base;
       n /= base;
   }
   rev

}

fn palindromes(base: u64) -> impl std::iter::Iterator<Item = u64> {

   let mut lower = 1;
   let mut upper = base;
   let mut next = 0;
   let mut even = false;
   std::iter::from_fn(move || {
       next += 1;
       if next == upper {
           if even {
               lower = upper;
               upper *= base;
           }
           next = lower;
           even = !even;
       }
       Some(match even {
           true => next * upper + reverse(base, next),
           _ => next * lower + reverse(base, next / base),
       })
   })

}

fn print_palindromic_primes(base: u64, limit: u64) {

   let width = (limit as f64).log(base as f64).ceil() as usize;
   let mut count = 0;
   let columns = 80 / (width + 1);
   println!("Base {} palindromic primes less than {}:", base, limit);
   for p in palindromes(base)
       .take_while(|x| *x < limit)
       .filter(|x| primal::is_prime(*x))
   {
       count += 1;
       print!(
           "{:>w$}",
           radix_fmt::radix(p, base as u8).to_string(),
           w = width
       );
       if count % columns == 0 {
           println!();
       } else {
           print!(" ");
       }
   }
   if count % columns != 0 {
       println!();
   }
   println!("Count: {}", count);

}

fn count_palindromic_primes(base: u64, limit: u64) {

   let c = palindromes(base)
       .take_while(|x| *x < limit)
       .filter(|x| primal::is_prime(*x))
       .count();
   println!(
       "Number of base {} palindromic primes less than {}: {}",
       base, limit, c
   );

}

fn main() {

   print_palindromic_primes(10, 1000);
   println!();
   print_palindromic_primes(10, 100000);
   println!();
   count_palindromic_primes(10, 1000000000);
   println!();
   print_palindromic_primes(16, 500);

}</lang>

Output:

Base 10 palindromic primes less than 1000:
  2   3   5   7  11 101 131 151 181 191 313 353 373 383 727 757 787 797 919 929
Count: 20

Base 10 palindromic primes less than 100000:
    2     3     5     7    11   101   131   151   181   191   313   353   373
  383   727   757   787   797   919   929 10301 10501 10601 11311 11411 12421
12721 12821 13331 13831 13931 14341 14741 15451 15551 16061 16361 16561 16661
17471 17971 18181 18481 19391 19891 19991 30103 30203 30403 30703 30803 31013
31513 32323 32423 33533 34543 34843 35053 35153 35353 35753 36263 36563 37273
37573 38083 38183 38783 39293 70207 70507 70607 71317 71917 72227 72727 73037
73237 73637 74047 74747 75557 76367 76667 77377 77477 77977 78487 78787 78887
79397 79697 79997 90709 91019 93139 93239 93739 94049 94349 94649 94849 94949
95959 96269 96469 96769 97379 97579 97879 98389 98689 
Count: 113

Number of base 10 palindromic primes less than 1000000000: 5953

Base 16 palindromic primes less than 500:
  2   3   5   7   b   d  11 101 151 161 191 1b1 1c1 
Count: 13

Sidef

<lang ruby>func palindromic_primes(upto, base = 10) {

   var list = []
   for (var p = 2; p <= upto; p = p.next_palindrome(base)) {
       list << p if p.is_prime
   }
   return list

}

say palindromic_primes(1000)

for n in (1..10) {

   var count = palindromic_primes(10**n).len
   say "There are #{count} palindromic primes <= 10^#{n}"

}</lang>

Output:

[2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929]
There are 4 palindromic primes <= 10^1
There are 5 palindromic primes <= 10^2
There are 20 palindromic primes <= 10^3
There are 20 palindromic primes <= 10^4
There are 113 palindromic primes <= 10^5
There are 113 palindromic primes <= 10^6
There are 781 palindromic primes <= 10^7
There are 781 palindromic primes <= 10^8
There are 5953 palindromic primes <= 10^9
There are 5953 palindromic primes <= 10^10

Wren

Library: Wren-math

Library: Wren-fmt

Library: Wren-seq

<lang ecmascript>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(99999) var pals = [] for (p in primes) {

   if (p == reversed.call(p)) pals.add(p)

} System.print("Palindromic primes under 1,000:") var smallPals = pals.where { |p| p < 1000 }.toList for (chunk in Lst.chunks(smallPals, 10)) Fmt.print("$3d", chunk) System.print("\n%(smallPals.count) such primes found.")

System.print("\nAdditional palindromic primes under 100,000:") var bigPals = pals.where { |p| p >= 1000 }.toList for (chunk in Lst.chunks(bigPals, 10)) Fmt.print("$,6d", chunk) System.print("\n%(bigPals.count) such primes found, %(pals.count) in all.")</lang>

Output:

Palindromic primes under 1,000:
  2   3   5   7  11 101 131 151 181 191
313 353 373 383 727 757 787 797 919 929

20 such primes found.

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

93 such primes found, 113 in all.

XPL0

<lang XPL0>func IsPrime(N); \Return 'true' if N is a prime number int N, I; [if N <= 1 then return false; for I:= 2 to sqrt(N) do

   if rem(N/I) = 0 then return false;

return true; ];

func Reverse(N); int N, M; [M:= 0; repeat N:= N/10;

       M:= M*10 + rem(0);

until N=0; return M; ];

int Count, N; [Count:= 0; for N:= 1 to 1000-1 do

   if N=Reverse(N) & IsPrime(N) then
       [IntOut(0, N);
       Count:= Count+1;
       if rem(Count/10) = 0 then CrLf(0) else ChOut(0, 9\tab\);
       ];

]</lang>

Output:

2       3       5       7       11      101     131     151     181     191
313     353     373     383     727     757     787     797     919     929