Iccanobif primes

Iccanobif primes are prime numbers that, when reversed, are a Fibonacci number.

Iccanobif 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 display the first 10 iccanobif primes.

Stretch

• Find and display the digit count of the next 15 iccanobif primes.

See also

• OEIS:A036797 - Iccanobif (or iccanobiF) primes: primes which are Fibonacci numbers when reversed

ALGOL 68

BEGIN # show the first 10 prime Iccanobif (reversed Fibonacci) numbers       #
    # returns n with the digits reversed                                     #
    OP REVERSE = ( INT n )INT:
       BEGIN
            INT reverse := 0;
            INT v       := ABS n;
            WHILE v > 0 DO
                reverse *:= 10 +:= v MOD 10;
                v OVERAB 10
            OD;
            reverse * SIGN n
       END # REVERSE # ;
    # returns TRUE if n is prime, FALSE otherwise - uses trial division      #
    PROC is prime = ( LONG INT n )BOOL:
         IF   n < 3       THEN n = 2
         ELIF n MOD 3 = 0 THEN n = 3
         ELIF NOT ODD n   THEN FALSE
         ELSE
             BOOL is a prime := TRUE;
             INT  f          := 5;
             INT  f2         := 25;
             INT  to next    := 24;
             WHILE f2 <= n AND is a prime DO
                 is a prime := n MOD f /= 0;
                 f         +:= 2;
                 f2        +:= to next;
                 to next   +:= 8
             OD;
             is a prime
         FI # is prime # ;
    # task                                                                   #
    INT p count := 0;
    INT prev    := 0;
    INT curr    := 1;
    WHILE p count < 10 DO
        INT next = prev + curr;
        prev    := curr;
        curr    := next;
        INT rev := REVERSE curr;
        IF is prime( rev ) THEN
            # have a prime iccanobif number #
            p count +:= 1;
            print( ( " ", whole( rev, 0 ) ) )
        FI
    OD
END

Output:

 2 3 5 31 43 773 7951 64901 52057 393121

Raku

sub abbr ($_) { (.chars < 41 ?? $_ !! .substr(0,20) ~ '..' ~ .substr(*-20)) ~ " (digits: {.chars})" }

say (++$).fmt('%2d') ~ ': ' ~ .flip.&abbr for (lazy (1,1,*+*…*).hyper.grep: {.flip.is-prime})[^25];

Output:

 1: 2 (digits: 1)
 2: 3 (digits: 1)
 3: 5 (digits: 1)
 4: 31 (digits: 2)
 5: 43 (digits: 2)
 6: 773 (digits: 3)
 7: 7951 (digits: 4)
 8: 64901 (digits: 5)
 9: 52057 (digits: 5)
10: 393121 (digits: 6)
11: 56577108676171 (digits: 14)
12: 940647607443258103531 (digits: 21)
13: 5237879497657222310489731409575442761 (digits: 37)
14: 9026258083384996860449366072142307801963 (digits: 40)
15: 19900335674812302969..34431012073266446403 (digits: 80)
16: 77841137362967479985..52312097783685331923 (digits: 104)
17: 37722585901567604188..29174997072830756131 (digits: 137)
18: 75736193894876131595..50767238644714305761 (digits: 330)
19: 17890336847332837620..13175300695235035913 (digits: 406)
20: 92327163101729115305..27061468856047302507 (digits: 409)
21: 50420157810698056253..67335124247362214481 (digits: 503)
22: 30511012474739380092..69296158361330018201 (digits: 888)
23: 46818547042693694555..08664543144645856321 (digits: 1020)
24: 87101347853037819884..20128396998865227391 (digits: 1122)
25: 17451656022543765336..20100243761843652461 (digits: 1911)
26: 48989340566288399474..02930339234215909399 (digits: 1947)
27: 12746927684958209654..53436989647994940101 (digits: 2283)
28: 35746826582658751012..25010735912438195633 (digits: 3727)
29: 87987175281297657706..48748727893681871587 (digits: 4270)
30: 81807376367113798363..13687506007959668569 (digits: 10527)

Wren

Library: Wren-gmp

Library: Wren-fmt

import "./gmp" for Mpz
import "./fmt" for Fmt

var fib = Mpz.new()
var p = Mpz.new()
var prev = Mpz.zero
var curr = Mpz.one
var count = 0
System.print("First 30 Iccanobif primes:")
while (count < 30) {
    fib.add(curr, prev)
    var fs = fib.toString
    p.setStr(fs[-1..0])
    if (p.probPrime(15) > 0) {
        count =  count + 1
        var pc = p.toString.count
        Fmt.print("$2d: $20a ($d digits)", count, p, pc)
    }
    prev.set(curr)
    curr.set(fib)
}

Output:

First 27 Iccanobif primes:
 1: 2 (1 digits)
 2: 3 (1 digits)
 3: 5 (1 digits)
 4: 31 (2 digits)
 5: 43 (2 digits)
 6: 773 (3 digits)
 7: 7951 (4 digits)
 8: 64901 (5 digits)
 9: 52057 (5 digits)
10: 393121 (6 digits)
11: 56577108676171 (14 digits)
12: 940647607443258103531 (21 digits)
13: 5237879497657222310489731409575442761 (37 digits)
14: 9026258083384996860449366072142307801963 (40 digits)
15: 19900335674812302969...34431012073266446403 (80 digits)
16: 77841137362967479985...52312097783685331923 (104 digits)
17: 37722585901567604188...29174997072830756131 (137 digits)
18: 75736193894876131595...50767238644714305761 (330 digits)
19: 17890336847332837620...13175300695235035913 (406 digits)
20: 92327163101729115305...27061468856047302507 (409 digits)
21: 50420157810698056253...67335124247362214481 (503 digits)
22: 30511012474739380092...69296158361330018201 (888 digits)
23: 46818547042693694555...08664543144645856321 (1020 digits)
24: 87101347853037819884...20128396998865227391 (1122 digits)
25: 17451656022543765336...20100243761843652461 (1911 digits)
26: 48989340566288399474...02930339234215909399 (1947 digits)
27: 12746927684958209654...53436989647994940101 (2283 digits)
28: 35746826582658751012...25010735912438195633 (3727 digits)
29: 87987175281297657706...48748727893681871587 (4270 digits)
30: 81807376367113798363...13687506007959668569 (10527 digits)