# Find prime n such that reversed n is also prime

Find prime n such 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.
Nearly Emirp Primes, which don't count palindromatic primes like 101.

## 11l

```F is_prime(a)
I a == 2
R 1B
I a < 2 | a % 2 == 0
R 0B
L(i) (3 .. Int(sqrt(a))).step(2)
I a % i == 0
R 0B
R 1B

L(n) 1..499
I is_prime(n) & is_prime(Int(reversed(String(n))))
print(n, 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
```

## Action!

```INCLUDE "H6:SIEVE.ACT"

BYTE FUNC IsPrimeAndItsReverse(INT i BYTE ARRAY primes)
INT rev
BYTE d

IF primes(i)=0 THEN
RETURN (0)
FI
rev=0
WHILE i#0
DO
d=i MOD 10
rev==*10
rev==+d
i==/10
OD
RETURN (primes(rev))

PROC Main()
DEFINE MAX="999"
BYTE ARRAY primes(MAX+1)
INT i,count=[0]

Put(125) PutE() ;clear the screen
Sieve(primes,MAX+1)
FOR i=2 TO 499
DO
IF IsPrimeAndItsReverse(i,primes) THEN
PrintI(i) Put(32)
count==+1
FI
OD
PrintF("%E%EThere are %I primes",count)
RETURN```
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

There are 34 primes
```

```with Ada.Text_Io;

procedure Reverse_Prime is

type Number is new Long_Integer range 0 .. Long_Integer'Last;
package Number_Io is new Ada.Text_Io.Integer_Io (Number);

function Is_Prime (A : Number) return Boolean is
D : Number;
begin
if A < 2       then return False; end if;
if A in 2 .. 3 then return True;  end if;
if A mod 2 = 0 then return False; end if;
if A mod 3 = 0 then return False; end if;
D := 5;
while D * D <= A loop
if A mod D = 0 then
return False;
end if;
D := D + 2;
if A mod D = 0 then
return False;
end if;
D := D + 4;
end loop;
return True;
end Is_Prime;

function Reverse_Num (N : Number) return Number is
N2  : Number := N;
Res : Number := 0;
begin
while N2 /= 0 loop
Res := 10 * Res;
Res := Res  + (N2 mod 10);
N2  := N2 / 10;
end loop;
return Res;
end Reverse_Num;

Count : Natural := 0;
begin
for N in Number range 1 .. 499 loop
if Is_Prime (N) and then Is_Prime (Reverse_Num (N)) then
Count := Count + 1;
Number_Io.Put (N, Width => 3); Put ("  ");
if Count mod 8 = 0 then
New_Line;
end if;
end if;
end loop;
New_Line;
Put_Line (Count'Image & " primes.");
end Reverse_Prime;
```
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
34 primes.```

## ALGOL 68

```BEGIN # find primes whose reversed digits are also prime         #
INT max number = 500;   # largest prime we will reverse      #
INT max prime  = 1 000; # enough primes to handle reversing  #
# max number                         #
[ 1 : max prime ]BOOL p; FOR n TO UPB p DO p[ n ] := ODD n OD;
FOR i FROM 3 BY 2 TO ENTIER sqrt( UPB p ) DO
IF p[ i ] THEN
FOR s FROM i * i BY i + i TO UPB p DO p[ s ] := FALSE OD
FI
OD;
p[ 1 ] := FALSE; p[ 2 ] := TRUE;
OP FMT = ( INT n )STRING: whole( n, 0 );
INT count := 0;
FOR n TO max number DO
IF p[ n ] THEN
INT r := n MOD 10;
INT v := n;
WHILE ( v OVERAB 10 ) > 0 DO
r *:= 10 +:= v MOD 10
OD;
IF p[ r ] THEN
print( ( " ", whole( n, -3 ) ) );
IF ( count +:= 1 ) MOD 10 = 0 THEN print( ( newline ) ) FI
FI
FI
OD;
print( ( newline, "Found ", whole( count, 0 )
, " reversable primes up to ", whole( max number, 0 )
)
)
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 up to 500```

## 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
```

## Arturo

```print
select 1..499 'x ->
and? [prime? x][prime? to :integer reverse to :string x]
```
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`

## 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
```

## BASIC

```10 DEFINT A-Z: MP=999: MX=500
15 MP=10^FIX(LOG(MX)/LOG(10)+1)
20 DIM C(MP): C(0)=-1: C(1)=-1
30 FOR P=2 TO SQR(MP)
40 FOR C=P+P TO MP STEP P: C(C)=-1: NEXT
50 NEXT
60 FOR N=1 TO MX: IF C(N) THEN 100
70 R=0: V=N
80 IF V>0 THEN R=10*R+V MOD 10: V=V\10: GOTO 80
90 IF NOT C(R) THEN PRINT N,
100 NEXT
```
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```

## bc

```define t(n) {
auto i, p
if (n == 2) return(1)
for (i = 0; n % (p = a[i]) != 0; ++i) if (p * p > n) return(1)
return(0)
}

define r(n) {
auto m
for (m = 0; n > 9; n /= 10) m = (n % 10 + m) * 10
return(m + n)
}

for (n = 2; n != 500; ++n) if (t(n) != 0) a[o++] = n

for (i = 0; i != o; ++i) if (t(r(n = a[i])) != 0) n
```

## BCPL

```get "libhdr"

let sieve(prime, n) be
\$(  0!prime := false
1!prime := false
for i = 2 to n do i!prime := true
for p = 2 to n/2 if p!prime
\$(  let c = p*2
while c <= n
\$(  c!prime := false
c := c+p
\$)
\$)
\$)

let reverse(n) = valof
\$(  let r=0
while n>0
\$(  r := 10*r + n rem 10
n := n/10
\$)
resultis r
\$)

let start() be
\$(  let prime = vec 999
sieve(prime, 999)
for i = 2 to 500
if i!prime & reverse(i)!prime do
writef("%N ",i)
wrch('*N')
\$)```
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`

## C

```#include <stdbool.h>
#include <stdio.h>

bool is_prime(unsigned int n) {
if (n < 2)
return false;
if (n % 2 == 0)
return n == 2;
if (n % 3 == 0)
return n == 3;
for (unsigned int p = 5; p * p <= n; p += 4) {
if (n % p == 0)
return false;
p += 2;
if (n % p == 0)
return false;
}
return true;
}

unsigned int reverse(unsigned int n) {
unsigned int rev = 0;
for (; n > 0; n /= 10)
rev = rev * 10 + n % 10;
return rev;
}

int main() {
unsigned int count = 0;
for (unsigned int n = 1; n < 500; ++n) {
if (is_prime(n) && is_prime(reverse(n)))
printf("%3u%c", n, ++count % 10 == 0 ? '\n' : ' ');
}
printf("\nCount = %u\n", count);
return 0;
}
```
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
Count = 34
```

## CLU

```sieve = proc (max: int) returns (array[bool])
prime: array[bool] := array[bool]\$fill(0,max+1,true)
prime[0] := false
prime[1] := false
for p: int in int\$from_to(2,max/2) do
if ~prime[p] then continue end
for c: int in int\$from_to_by(p*p,max,p) do
prime[c] := false
end
end
return(prime)
end sieve

reverse = proc (n: int) returns (int)
r: int := 0
while n>0 do
r := 10*r + n//10
n := n/10
end
return(r)
end reverse

start_up = proc ()
po: stream := stream\$primary_output()
prime: array[bool] := sieve(999)

for i: int in int\$from_to(2, 500) do
if prime[i] cand prime[reverse(i)] then
stream\$puts(po, int\$unparse(i) || " ")
end
end
end start_up```
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`

## Cowgol

```include "cowgol.coh";

const PRIME_LIMIT := 999;
const LIMIT := 500;

var prime: uint8[PRIME_LIMIT + 1];
typedef P is @indexof prime;
sub sieve() is
prime[0] := 0;
prime[1] := 0;
MemSet(&prime[2], 0xFF, @bytesof prime-2);
var p: P := 2;
while p*p <= PRIME_LIMIT loop
if prime[p] != 0 then
var c := p*p;
while c <= PRIME_LIMIT loop
prime[c] := 0;
c := c + p;
end loop;
end if;
p := p + 1;
end loop;
end sub;

sub reverse(n: P): (r: P) is
r := 0;
while n>0 loop
r := 10*r + n%10;
n := n/10;
end loop;
end sub;

sieve();
var n: P := 1;
while n <= LIMIT loop
if prime[n] != 0 and prime[reverse(n)] != 0 then
print_i32(n as uint32);
print_char(' ');
end if;
n := n + 1;
end loop;
print_nl();```
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`

## 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...');
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
```

## Forth

Works with: Gforth
```: prime? ( n -- ? ) here + c@ 0= ;
: not-prime! ( n -- ) here + 1 swap c! ;

: prime-sieve ( n -- )
here over erase
0 not-prime!
1 not-prime!
2
begin
2dup dup * >
while
dup prime? if
2dup dup * do
i not-prime!
dup +loop
then
1+
repeat
2drop ;

: reverse ( n -- n )
0 swap
begin
dup 0 >
while
10 /mod swap rot 10 * + swap
repeat drop ;

: main
1000 prime-sieve
0
500 1 do
i prime? if i reverse prime? if
1 +
i 3 .r
dup 10 mod 0= if cr else space then
then then
loop
cr ." Count: " . cr ;

main
bye
```
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
Count: 34
```

## 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`

## Frink

`select[primes[2,500], {|n| isPrime[parseInt[join["", reverse[integerDigits[n]]]]]}]`
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 -> 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```

## J

```   (#~ 1 p: |.&.":"0) i.&.(p:inv) 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
```

## jq

Works with: jq

Works with gojq, the Go implementation of jq

Using the definition of is_prime at Erdős-primes#jq:

```# Generate a stream of reversible primes.
# If . is null the stream is unbounded;
# otherwise only integers less than . are considered.

def reversible_primes:
def r: tostring|explode|reverse|implode|tonumber;
(if . == null then infinite else . end) as \$n
| 2, (range(3; \$n; 2) | select(is_prime and (r|is_prime)));

"Primes under 500 which are also primes when the digits are reversed:",
(500 | reversible_primes)```
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
```

## Julia

```using Primes

let

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
```

## Mathematica/Wolfram Language

```Select[Range[499], PrimeQ[#] \[And] PrimeQ[IntegerReverse[#]] &]
```
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}`

## Lua

```do  -- find primes whose reversed digits are also prime
local function isPrime( p )
if p <= 1 or p % 2 == 0 then
return p == 2
else
local prime = true
local i     = 3
local rootP = math.floor( math.sqrt( p ) )
while i <= rootP and prime do
prime = p % i ~= 0
i     = i + 2
end
return prime
end
end
local function reverseDigits( n )
end
local count = 0
for n = 1,500 do
if isPrime( n ) then
if isPrime( reverseDigits( n ) ) then
count = count + 1
io.write( string.format( "%3d", n ), count % 10 == 0 and "\n" or " " )
end
end
end
io.write( "\nFound ", count, " reversable primes up to 500" )
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 up to 500
```

```            NORMAL MODE IS INTEGER
BOOLEAN PRIME
DIMENSION PRIME(1000)
VECTOR VALUES FMT = \$I3*\$

PRIME(0)=0B
PRIME(1)=0B
THROUGH INIT, FOR P=2, 1, P.GE.1000
INIT        PRIME(P)=1B

THROUGH SIEVE, FOR P=2, 1, P.GE.32
THROUGH SIEVE, FOR C=P*P, P, C.GE.1000
SIEVE       PRIME(C)=0B

THROUGH TEST, FOR N=2, 1, N.GE.500
WHENEVER .NOT. PRIME(N), TRANSFER TO TEST
NN=N
R=0
RVRSE       WHENEVER NN.G.0
NXT=NN/10
R=R*10+NN-NXT*10
NN=NXT
TRANSFER TO RVRSE
END OF CONDITIONAL
WHENEVER .NOT. PRIME(R), TRANSFER TO TEST
PRINT FORMAT FMT,N
TEST        CONTINUE
END OF PROGRAM```
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```

## Modula-2

```MODULE ReversePrime;
FROM InOut IMPORT WriteCard, WriteLn;

CONST
Primes = 1000;
Max = 500;

VAR prime: ARRAY [1..Primes] OF BOOLEAN;
n, col: CARDINAL;

PROCEDURE reverse(n: CARDINAL): CARDINAL;
VAR r: CARDINAL;
BEGIN
r := 0;
WHILE n > 0 DO
r := r*10 + n MOD 10;
n := n DIV 10;
END;
RETURN r;
END reverse;

PROCEDURE Sieve;
VAR i, j: CARDINAL;
BEGIN
prime[1] := FALSE;
FOR i := 2 TO Primes DO
prime[i] := TRUE;
END;
FOR i := 2 TO Primes DIV 2 DO
j := i*2;
WHILE j <= Primes DO
prime[j] := FALSE;
j := j + i;
END;
END;
END Sieve;

BEGIN
Sieve();
col := 0;
FOR n := 2 TO Max DO
IF prime[n] AND prime[reverse(n)] THEN
WriteCard(n,5);
col := col + 1;
IF col MOD 8 = 0 THEN
WriteLn();
END;
END;
END;
WriteLn();
END ReversePrime.
```
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```

## Nim

```import math, strutils

const
N1 = 499    # Limit for the primes.
N2 = 999    # Limit for the reverses of primes.

# Sieve of Erathosthenes.
var composite: array[2..N2, bool]     # Default is false.
for p in 2..sqrt(N2.toFloat).int:
if not composite[p]:
for k in countup(p * p, N2, p):
composite[k] = true

template isPrime(n: int): bool = not composite[n]

func reversed(n: int): int =
var n = n
while n != 0:
result = 10 * result + n mod 10
n = n div 10

var result: seq[int]
for n in 2..N1:
if n.isPrime and reversed(n).isPrime:

for i, n in result:
stdout.write (\$n).align(3)
stdout.write if (i + 1) mod 10 == 0: '\n' else: ' '
echo()
```
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 ```

## OCaml

Using the function `seq_primes` from Extensible prime generator#OCaml:

```let int_reverse =
let rec loop m n =
if n < 10 then m + n else loop ((m + n mod 10) * 10) (n / 10)
in loop 0

let is_prime n =
let not_divisible x = n mod x <> 0 in
seq_primes |> Seq.take_while (fun x -> x * x <= n) |> Seq.for_all not_divisible

let () =
seq_primes |> Seq.filter (fun p -> is_prime (int_reverse p))
|> Seq.take_while ((>) 500) |> Seq.iter (Printf.printf " %u") |> print_newline
```
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`

## 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.
```

## Python

```#!/usr/bin/python

def isPrime(n):
for i in range(2, int(n**0.5) + 1):
if n % i == 0:
return False
return True

def isBackPrime(n):
if not isPrime(n):
return False
m = 0
while n:
m *= 10
m += n % 10
n //= 10
return isPrime(m)

if __name__ == '__main__':
for n in range(2, 499):
if isBackPrime(n):
print(n, 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`

## PILOT

```C :n=1
*number
C :p=n
U :*prime
J (pr=0):*next
U :*rev
C :p=r
U :*prime
T (pr):#n
*next
C :n=n+1
J (n<500):*number
E :

*rev
C :r=0
*digit
C :z=p/10
:r=r*10+(p-z*10)
:p=z
J (z):*digit
E :

*prime
C :pr=0
E (p=1):
C :pr=1
E (p<4):
C :pr=0
E (p=2*(p/2)):
C :i=3
*div
E (p=i*(p/i)):
C :i=i+2
J (i<p/2):*div
C :pr=1
E :```
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```

## PL/I

```reversePrimes: procedure options(main);
declare prime(1:999) bit;

sieve: procedure;
declare (i,j,hi) fixed;
hi = hbound(prime,1);
prime(1) = '0'b;
do i=2 to hi; prime(i) = '1'b; end;
do i=2 to sqrt(hi);
do j=i*i to hi by i; prime(j) = '0'b; end;
end;
end sieve;

reverse: procedure(nn) returns(fixed);
declare (n, nn, r) fixed;
r=0;
do n=nn repeat(n/10) while (n>0);
r = 10*r + mod(n,10);
end;
return(r);
end reverse;

declare (n, found) fixed;
call sieve;
found = 0;
do n=1 to 499;
if prime(n) & prime(reverse(n)) then do;
put edit(n) (F(4));
found = found + 1;
if mod(found,20) = 0 then put skip;
end;
end;

put skip list('Reverse primes found:',found);
end reversePrimes;```
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
Reverse primes found:        34```

## PL/M

Works with: 8080 PL/M Compiler
... under CP/M (or an emulator)
```100H: /* FIND PRIMES THAT ARE STILL PRIME WHEN THEIR DIGITS ARE REVERSED     */

/* CP/M BDOS SYSTEM CALL                                                  */
BDOS: PROCEDURE( FN, ARG ); DECLARE FN BYTE, ARG ADDRESS; GOTO 5; END;
/* I/O ROUTINES                                                           */
PR\$CHAR:   PROCEDURE( C ); DECLARE C BYTE;    CALL BDOS( 2, C );  END;
PR\$STRING: PROCEDURE( S ); DECLARE S ADDRESS; CALL BDOS( 9, S );  END;
PR\$NL:     PROCEDURE;   CALL PR\$CHAR( 0DH ); CALL PR\$CHAR( 0AH ); END;
PR\$NUMBER: PROCEDURE( N ); /* PRINTS A NUMBER IN THE MINIMUN FIELD WIDTH  */
DECLARE V ADDRESS, N\$STR ( 6 )BYTE, W BYTE;
V = N;
W = LAST( N\$STR );
N\$STR( W ) = '\$';
N\$STR( W := W - 1 ) = '0' + ( V MOD 10 );
DO WHILE( ( V := V / 10 ) > 0 );
N\$STR( W := W - 1 ) = '0' + ( V MOD 10 );
END;
CALL PR\$STRING( .N\$STR( W ) );
END PR\$NUMBER;

/* RETURNS TRUE IF N IS PRIME, FALSE OTHERWISE, USES TRIAL DIVISION      */
IS\$PRIME: PROCEDURE( N )BYTE;
DECLARE PRIME BYTE;
IF      N < 3       THEN PRIME = N = 2;
ELSE IF N MOD 3 = 0 THEN PRIME = N = 3;
ELSE IF N MOD 2 = 0 THEN PRIME = 0;
ELSE DO;
DECLARE ( F, F2, TO\$NEXT ) ADDRESS;
PRIME   = 1;
F       = 5;
F2      = 25;
TO\$NEXT = 24;            /* NOTE: ( 2N + 1 )^2 - ( 2N - 1 )^2 = 8N */
DO WHILE F2 <= N AND PRIME;
PRIME   = N MOD F <> 0;
F       = F + 2;
F2      = F2 + TO\$NEXT;
TO\$NEXT = TO\$NEXT + 8;
END;
END;
RETURN PRIME;
END IS\$PRIME;

REVERSE: PROCEDURE( N )ADDRESS;  /* RETURNS THE REVERSED DIGITS OF N */
DECLARE ( R, V ) ADDRESS;
V = N;
R = V MOD 10;
DO WHILE( ( V := V / 10 ) > 0 );
R = ( R * 10 ) + ( V MOD 10 );
END;
RETURN R;
END REVERSE ;

/* FIND THE NUMBERS UP TO 500                                             */

DECLARE ( I, COUNT ) ADDRESS;

COUNT = 0;
DO I = 1 TO 500;
IF IS\$PRIME( I ) THEN DO;
IF IS\$PRIME( REVERSE( I ) ) THEN DO;
IF I <  10 THEN CALL PR\$CHAR( ' ' );
IF I < 100 THEN CALL PR\$CHAR( ' ' );
CALL PR\$NUMBER( I );
IF ( COUNT := COUNT + 1 )  MOD 20 = 0 THEN CALL PR\$NL;
ELSE CALL PR\$CHAR( ' ' );
END;
END;
END;

EOF```
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
```

## Quackery

`eratosthenes` and `isprime` are defined at Sieve of Eratosthenes#Quackery.

```  1000 eratosthenes

[ number\$ reverse \$->n drop ] is revnum     ( n --> n )

[ dup isprime iff
[ revnum isprime ]
else [ drop false ] ]       is isrevprime ( n --> b )

[] [] 500 times
[ i^ isrevprime if
[ i^ join ] ]
witheach [ number\$ nested join ]
60 wrap\$```
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
```

## 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 j=@.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...
```

## RPL

This program uses the words `RVSTR` and `BPRIM?`, respectively made to revert a string and to test primality by trial division

```≪ { } 1 499 FOR n
IF n R→B 'BPRIM? THEN
IF n →STR RVSTR STR→ R→B BPRIM? THEN n + END
END
NEXT
```

#### Straightforward approach

Numbers are here reversed without any string conversion.

Works with: HP version 49
```« { }
1 499 FOR n
IF n ISPRIME? THEN
n 0
WHILE OVER REPEAT
SWAP 10 IDIV2 ROT 10 * +
END NIP
IF ISPRIME? THEN n + END
END
NEXT
```
Output:
```1: { 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 }
```

## Ruby

```p Prime.each(500).select{|pr| pr.digits.join.to_i.prime? }
```
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]
```

## Rust

```use prime_tools ;

fn myreverse( n : u32 ) -> u32 {
let forward : String = n.to_string( ) ;
let numberstring = &forward[..] ;
let mut reversed : String = String::new( ) ;
for c in numberstring.chars( ).rev( ) {
reversed.push( c ) ;
}
*&reversed[..].parse::<u32>( ).unwrap( )
}

fn main() {
let mut reversible_primes : Vec<u32> = Vec::new( ) ;
for num in 2..=500 {
if prime_tools::is_u32_prime( num ) && prime_tools::is_u32_prime(
myreverse( num ))  {
reversible_primes.push( num ) ;
}
}
println!("{:?}" , reversible_primes ) ;
}
```
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]
```

## Seed7

```\$ include "seed7_05.s7i";

const func boolean: isPrime (in integer: number) is func
result
var boolean: prime is FALSE;
local
var integer: upTo is 0;
var integer: testNum is 3;
begin
if number = 2 then
prime := TRUE;
elsif odd(number) and number > 2 then
upTo := sqrt(number);
while number rem testNum <> 0 and testNum <= upTo do
testNum +:= 2;
end while;
prime := testNum > upTo;
end if;
end func;

const func integer: revDigits (in var integer: number) is func
result
var integer: revNum is 0;
begin
while number > 0 do
revNum *:= 10;
revNum +:= number rem 10;
number := number div 10;
end while;
end func;

const func boolean: isRevPrime (in integer: number) is
return isPrime(number) and isPrime(revDigits(number));

const proc: main is func
local
var integer: number is 0;
var integer: count is 0;
begin
for number range 1 to 499 do
if isRevPrime(number) then
write(number <& " ");
incr(count);
end if;
end for;
writeln;
writeln("Found " <& count <& " reverse primes < 500.");
end func;```
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 reverse primes < 500.
```

## Sidef

```say primes(500).grep { .reverse.is_prime }
```
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]
```

## Wren

Library: Wren-math
Library: Wren-fmt
```import "./math" for Int
import "./fmt" for Fmt

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) {
}
System.print("Primes under 500 which are also primes when the digits are reversed:")
Fmt.tprint("\$3d", reversedPrimes, 17)
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.
```

## 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);        \Return the reverse of the digits in N
int  N, M;
[M:= 0;
while N do
[N:= N/10;
M:= M*10 + rem(0);
];
return M;
];

int Count, N;
[Count:= 0;
for N:= 1 to 499 do
[if IsPrime(N) & IsPrime(Reverse(N)) then
[IntOut(0, N);
Count:= Count+1;
if rem(Count/10) = 0 then CrLf(0) else ChOut(0, 9\tab\);
]
];
CrLf(0);
IntOut(0, Count);
Text(0, " reversible primes found.");
]```
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
34 reversible primes found.
```