I'm working on modernizing Rosetta Code's infrastructure. Starting with communications. Please accept this time-limited open invite to RC's Slack.. --Michael Mol (talk) 20:59, 30 May 2020 (UTC)

# 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.

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 )    endend.`
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.AWKBEGIN {    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: 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., 2021let 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? ] filterdup length "Found %d reverse primes < 500.\n\n" printf10 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 nprint`
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.
```

`import Data.List (intercalate, transpose)import Data.List.Split (chunksOf)import Data.Numbers.Primes (isPrime, primes)import Text.Printf (printf) ------------------------ PREDICATE ----------------------- p :: Int -> Boolp 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]] -> Stringtable 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.*/saysay '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 = 0num = 0limit = 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" + nlsee "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 Intimport "/fmt" for Fmtimport "/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.
```