First 9 prime Fibonacci number

From Rosetta Code
First 9 prime Fibonacci number 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


Show on this page the first 9 prime Fibonacci numbers.

Ada[edit]

with Ada.Text_IO;

procedure Prime_Fibonacci is

   function Is_Prime (A : Natural) return Boolean is
      D : Natural;
   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;

   F_1   : Natural := 0;
   F_2   : Natural := 1;

   function Fibonacci return Natural is
      R : Natural := F_1 + F_2;
   begin
      F_1 := F_2;
      F_2 := R;
      return R;
   end Fibonacci;

   Count : Natural := 0;
   Fib   : Natural;
begin
   while Count < 9 loop
      Fib := Fibonacci;
      if Is_Prime (Fib) then
         Count := Count + 1;
         Ada.Text_IO.Put_Line (Fib'Image);
      end if;
   end loop;
end Prime_Fibonacci;
Output:
 2
 3
 5
 13
 89
 233
 1597
 28657
 514229

ALGOL 68[edit]

BEGIN # show the first 9 prime fibonacci numbers #
    PR read "primes.incl.a68" PR # include prime utilities #
    INT p count := 0;
    INT prev    := 0;
    INT curr    := 1;
    WHILE p count < 9 DO
        INT next = prev + curr;
        prev    := curr;
        curr    := next;
        IF is probably prime( curr ) THEN
            # have a prime fibonacci number #
            p count +:= 1;
            print( ( " ", whole( curr, 0 ) ) )
        FI
    OD
END
Output:
 2 3 5 13 89 233 1597 28657 514229

ALGOL W[edit]

begin % -- show the first 9 prime fibonacci numbers %

    % -- returns true if n is prime, false otherwise - uses trial division %
    logical procedure isPrime ( integer value n ) ;
        if      n < 3        then n = 2
        else if not odd( n ) then false
        else begin
            logical prime;
            prime := true;
            for i := 3 step 2 until entier( sqrt( n ) ) do begin
                prime := n rem i not = 0;
                if not prime then goto endTest;
            end for_i;
endTest:    prime
        end isPrime ;

    begin % -- task %
        integer pCount, prev, curr, next;
        pCount := 0;
        prev   := 0;
        curr   := 1;
        while pCount < 9 do begin
            next := prev + curr;
            prev := curr;
            curr := next;
            if isPrime( curr ) then begin
                pCount := pCount + 1;
                writeon( i_w := 1, s_w := 0, " ", curr )
            end if_isPrime__curr
        end while_pCount_lt_9
    end task
end.
Output:
 2 3 5 13 89 233 1597 28657 514229

AWK[edit]

# syntax: GAWK -f FIRST_9_PRIME_FIBONACCI_NUMBER.AWK
BEGIN {
    f1 = f2 = 1
    stop = 9
    printf("First %d Prime Fibonacci numbers:\n",stop)
    while (count < stop) {
      f3 = f1 + f2
      if (is_prime(f3)) {
        printf("%d ",f3)
        count++
      }
      f1 = f2
      f2 = f3
    }
    printf("\n")
    exit(0)
}
function is_prime(n,  d) {
    d = 5
    if (n < 2) { return(0) }
    if (n % 2 == 0) { return(n == 2) }
    if (n % 3 == 0) { return(n == 3) }
    while (d*d <= n) {
      if (n % d == 0) { return(0) }
      d += 2
      if (n % d == 0) { return(0) }
      d += 4
    }
    return(1)
}
Output:
First 9 Prime Fibonacci numbers:
2 3 5 13 89 233 1597 28657 514229


BASIC[edit]

BASIC256[edit]

function isPrime(v)
	if v < 2 then return False
	if v mod 2 = 0 then return v = 2
	if v mod 3 = 0 then return v = 3
	d = 5
	while d * d <= v
		if v mod d = 0 then return False else d += 2
	end while
	return True
end function

function fib(nr)
	if nr = 0 then return 0
	if nr = 1 then return 1
	if nr > 1 then return fib(nr-1) + fib(nr-2)
end function

i = 0
cont = 0
print "The first 9 Prime Fibonacci numbers: "
while True
	i += 1
	num = fib(i)
	if isPrime(num) then
		cont += 1
		if cont < 10 then
			print num; " ";
		else
			exit while
		end if
	end if
end while
end
Output:
Igual que la entrada de FreeBASIC.

FreeBASIC[edit]

Function isPrime(Byval ValorEval As Integer) As Boolean
    If ValorEval <= 1 Then Return False
    For i As Integer = 2 To Int(Sqr(ValorEval))
        If ValorEval Mod i = 0 Then Return False
    Next i
    Return True
End Function

Function fib(nr As Integer) As Integer
    If nr = 0 Then Return 0
    If nr = 1 Then Return 1
    If nr > 1 Then Return fib(nr-1) + fib(nr-2)
End Function

Dim As Integer i = 0, num, cont = 0
Print "The first 9 Prime Fibonacci numbers: "
Do
    i += 1
    num = fib(i)
    If isprime(num) Then
        cont += 1
        If cont < 10 Then
            Print num; " ";
        Else
            Exit Do
        End If
    End If
Loop
Sleep
Output:
The first 9 Prime Fibonacci numbers: 
2  3  5  13  89  233  1597  28657  514229

PureBasic[edit]

Procedure isPrime(v.i)
  If     v <= 1    : ProcedureReturn #False
  ElseIf v < 4     : ProcedureReturn #True
  ElseIf v % 2 = 0 : ProcedureReturn #False
  ElseIf v < 9     : ProcedureReturn #True
  ElseIf v % 3 = 0 : ProcedureReturn #False
  Else
    Protected r = Round(Sqr(v), #PB_Round_Down)
    Protected f = 5
    While f <= r
      If v % f = 0 Or v % (f + 2) = 0
        ProcedureReturn #False
      EndIf
      f + 6
    Wend
  EndIf
  ProcedureReturn #True
EndProcedure

Procedure fib(nr.i)
  If     nr = 0 : ProcedureReturn 0
  ElseIf nr = 1 : ProcedureReturn 1
  ElseIf nr > 1 : ProcedureReturn fib(nr-1) + fib(nr-2)
  EndIf
EndProcedure

If OpenConsole()
  Define i.i = 0, cont.i = 0
  PrintN("The first 9 Prime Fibonacci numbers: ")
  Repeat
    i + 1
    num = fib(i)
    If isprime(num)
      cont + 1
      If cont < 10
        Print(Str(num) + " ")
      Else
        Break
      EndIf
    EndIf
  ForEver
  
  PrintN(#CRLF$ + "--- terminado, pulsa RETURN---"): Input()
  CloseConsole()
EndIf
Output:
Igual que la entrada de FreeBASIC.

Yabasic[edit]

sub isPrime(v)
    if v < 2 then return False : fi
    if mod(v, 2) = 0 then return v = 2 : fi
    if mod(v, 3) = 0 then return v = 3 : fi
    d = 5
    while d * d <= v
        if mod(v, d) = 0 then return False else d = d + 2 : fi
    wend
    return True
end sub

sub fib(nr)
    if nr = 0 then return 0 : fi
    if nr = 1 then return 1 : fi
    if nr > 1 then return fib(nr-1) + fib(nr-2) : fi
end sub

i = 0
cont = 0
print "The first 9 Prime Fibonacci numbers: "
do
    i = i + 1
    num = fib(i)
    if isPrime(num) then
        cont = cont + 1
        if cont < 10 then
            print num, " ";
        else
            break
        end if
    end if
loop
end
Output:
Igual que la entrada de FreeBASIC.


C[edit]

Translation of: Wren

Requires C99 or later.

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

bool isPrime(uint64_t n) {
    if (n < 2) return false;
    if (!(n%2)) return n == 2;
    if (!(n%3)) return n == 3;
    uint64_t d = 5;
    while (d*d <= n) {
        if (!(n%d)) return false;
        d += 2;
        if (!(n%d)) return false;
        d += 4;
    }
    return true;
}

int main() {
    uint64_t f1 = 1, f2 = 1, f3;
    int count = 0, limit = 12; // as far as we can get without using GMP
    printf("The first %d prime Fibonacci numbers are:\n", limit);
    while (count < limit) {
        f3 = f1 + f2;
        if (isPrime(f3)) {
            printf("%ld ", f3);
            count++;
        }
        f1 = f2;
        f2 = f3;
    }
    printf("\n");
    return 0;
}
Output:
The first 12 prime Fibonacci numbers are:
2 3 5 13 89 233 1597 28657 514229 433494437 2971215073 99194853094755497 

C++[edit]

Library: GMP
Library: Primesieve
#include <chrono>
#include <iostream>
#include <sstream>
#include <utility>
#include <primesieve.hpp>
#include <gmpxx.h>

using big_int = mpz_class;

bool is_probably_prime(const big_int& n) {
    return mpz_probab_prime_p(n.get_mpz_t(), 30) != 0;
}

class prime_fibonacci_generator {
public:
    prime_fibonacci_generator();
    std::pair<uint64_t, big_int> next();
private:
    big_int next_fibonacci();
    primesieve::iterator p_;
    big_int f0_ = 0;
    big_int f1_ = 1;
    uint64_t n_ = 0;
};

prime_fibonacci_generator::prime_fibonacci_generator() {
    for (int i = 0; i < 2; ++i)
        p_.next_prime();
}

std::pair<uint64_t, big_int> prime_fibonacci_generator::next() {
    for (;;) {
        if (n_ > 4) {
            uint64_t p = p_.next_prime();
            for (; p > n_; ++n_)
                next_fibonacci();
        }
        ++n_;
        big_int f = next_fibonacci();
        if (is_probably_prime(f))
            return {n_ - 1, f};
    }
}

big_int prime_fibonacci_generator::next_fibonacci() {
    big_int result = f0_;
    big_int f = f0_ + f1_;
    f0_ = f1_;
    f1_ = f;
    return result;
}

std::string to_string(const big_int& n) {
    std::string str = n.get_str();
    if (str.size() > 40) {
        std::ostringstream os;
        os << str.substr(0, 20) << "..." << str.substr(str.size() - 20) << " ("
           << str.size() << " digits)";
        return os.str();
    }
    return str;
}

int main() {
    auto start = std::chrono::high_resolution_clock::now();
    prime_fibonacci_generator gen;
    for (int i = 1; i <= 26; ++i) {
        auto [n, f] = gen.next();
        std::cout << i << ": F(" << n << ") = " << to_string(f) << '\n';
    }
    auto finish = std::chrono::high_resolution_clock::now();
    std::chrono::duration<double> ms(finish - start);
    std::cout << "elapsed time: " << ms.count() << " seconds\n";
}
Output:
1: F(3) = 2
2: F(4) = 3
3: F(5) = 5
4: F(7) = 13
5: F(11) = 89
6: F(13) = 233
7: F(17) = 1597
8: F(23) = 28657
9: F(29) = 514229
10: F(43) = 433494437
11: F(47) = 2971215073
12: F(83) = 99194853094755497
13: F(131) = 1066340417491710595814572169
14: F(137) = 19134702400093278081449423917
15: F(359) = 47542043773469822074...62268716376935476241 (75 digits)
16: F(431) = 52989271100609562179...55134424689676262369 (90 digits)
17: F(433) = 13872771278047838271...25954602593712568353 (91 digits)
18: F(449) = 30617199924845450305...49015933442805665949 (94 digits)
19: F(509) = 10597999265301490732...54396195769876129909 (107 digits)
20: F(569) = 36684474316080978061...15228143777781065869 (119 digits)
21: F(571) = 96041200618922553823...31637646183008074629 (119 digits)
22: F(2971) = 35710356064190986072...48642001438470316229 (621 digits)
23: F(4723) = 50019563612695729290...02854387700053591957 (987 digits)
24: F(5387) = 29304412869392580554...82040327194725855833 (1126 digits)
25: F(9311) = 34232086066590238613...37580645424669476289 (1946 digits)
26: F(9677) = 10565977873308861656...95169792504550670357 (2023 digits)
elapsed time: 21.8042 seconds

CLU[edit]

fibonacci = iter () yields (int)
    a: int := 1
    b: int := 1
    while true do   
        yield(a)
        a, b := b, a+b
    end
end fibonacci

prime = proc (n: int) returns (bool)
    if n <= 4 then return(n=2 cor n=3) end
    if n//2=0 cor n//3=0 then return(false) end
    
    d: int := 5
    while d*d <= n do
        if n//d=0 then return(false) end
        d := d+2
        if n//d=0 then return(false) end
        d := d+4
    end
    return(true)
end prime

start_up = proc ()
    po: stream := stream$primary_output()
    seen: int := 0
    for n: int in fibonacci() do
        if seen=9 then break end
        if prime(n) then
            stream$putl(po, int$unparse(n))
            seen := seen+1
        end
    end
end start_up
Output:
2
3
5
13
89
233
1597
28657
514229

COBOL[edit]

       IDENTIFICATION DIVISION.
       PROGRAM-ID. PRIME-FIBONACCI.
       
       DATA DIVISION.
       WORKING-STORAGE SECTION.
       01 FIBONACCI-VARS.
          03 FIB                PIC 9(6).
          03 FIB-B              PIC 9(6).
          03 FIB-C              PIC 9(6).
          03 FIB-OUT            PIC Z(5)9.
       01 PRIME-VARS.   
          03 PRIME-FLAG         PIC X.
             88 PRIME           VALUE 'X'.
          03 DSOR               PIC 9(4).
          03 DSOR-SQ            PIC 9(6).
          03 DIV-RSLT           PIC 9(6)V9(3).
          03 FILLER             REDEFINES DIV-RSLT.
             05 FILLER          PIC 9(6).
             05 FILLER          PIC 9(3).
                88 DIVISIBLE    VALUE ZERO.
          
       PROCEDURE DIVISION.
       BEGIN.
           MOVE 1 TO FIB, FIB-B.
           PERFORM FIND-PRIME-FIBONACCI 9 TIMES.
           STOP RUN.
       
       FIND-PRIME-FIBONACCI.
           ADD FIB, FIB-B GIVING FIB-C.
           MOVE FIB-B TO FIB.
           MOVE FIB-C TO FIB-B.
           PERFORM CHECK-PRIME.
           IF NOT PRIME, GO TO FIND-PRIME-FIBONACCI.
           MOVE FIB TO FIB-OUT.
           DISPLAY FIB-OUT.
       
       CHECK-PRIME SECTION.
       BEGIN.
           MOVE SPACE TO PRIME-FLAG.
           IF FIB IS LESS THAN 5, GO TO TRIVIAL-PRIME.
           DIVIDE FIB BY 2 GIVING DIV-RSLT.
           IF DIVISIBLE, GO TO DONE.
           DIVIDE FIB BY 3 GIVING DIV-RSLT.
           IF DIVISIBLE, GO TO DONE.
           MOVE 5 TO DSOR.
           MOVE 25 TO DSOR-SQ.
           MOVE 'X' TO PRIME-FLAG.
           PERFORM TEST-DIVISOR 
           UNTIL NOT PRIME OR DSOR-SQ IS GREATER THAN FIB.
           GO TO DONE.
           
       TEST-DIVISOR.
           DIVIDE FIB BY DSOR GIVING DIV-RSLT.
           IF DIVISIBLE, MOVE SPACE TO PRIME-FLAG.
           ADD 2 TO DSOR.
           DIVIDE FIB BY DSOR GIVING DIV-RSLT.
           IF DIVISIBLE, MOVE SPACE TO PRIME-FLAG.
           ADD 4 TO DSOR.
           MULTIPLY DSOR BY DSOR GIVING DSOR-SQ.
       
       TRIVIAL-PRIME.
           IF FIB IS EQUAL TO 2 OR 3, MOVE 'X' TO PRIME-FLAG.
       DONE.
           EXIT.
Output:
     2
     3
     5
    13
    89
   233
  1597
 28657
514229

Comal[edit]

0010 FUNC prime(n) CLOSED
0020   IF n<4 THEN RETURN n=2 OR n=3
0030   IF n MOD 2=0 OR n MOD 3=0 THEN RETURN FALSE
0040   d:=5
0050   WHILE d*d<=n DO
0060     IF n MOD d=0 THEN RETURN FALSE
0070     d:+2
0080     IF n MOD d=0 THEN RETURN FALSE
0090     d:+4
0100   ENDWHILE
0110   RETURN TRUE
0120 ENDFUNC prime
0130 //
0140 found:=0
0150 a:=1;b:=1
0160 WHILE found<9 DO
0170   IF prime(a) THEN
0180     PRINT a
0190     found:+1
0200   ENDIF
0210   c:=a+b;a:=b;b:=c
0220 ENDWHILE
0230 END
Output:
2
3
5
13
89
233
1597
28657
514229

Cowgol[edit]

include "cowgol.coh";

sub prime(n: uint32): (p: uint8) is
    p := 0;
    if n <= 4 then
        if n==2 or n==3 then 
            p := 1; 
        end if;
    elseif n&1 != 0 and n%3 != 0 then
        var d: uint32 := 5;
        while d*d <= n loop
            if n%d == 0 then return; end if;
            d := d + 2;
            if n%d == 0 then return; end if;
            d := d + 4;
        end loop;
        p := 1;
    end if;
end sub;

var a: uint32 := 1;
var b: uint32 := 1;
var n: uint8 := 0;

while n<9 loop
    if prime(a) != 0 then
        print_i32(a);
        print_nl();
        n := n+1;
    end if;
    var c := a + b;
    a := b;
    b := c;
end loop;
Output:
2
3
5
13
89
233
1597
28657
514229

Draco[edit]

proc nonrec prime(ulong n) bool:
    bool comp;
    ulong d;
    if n <= 4 then n=2 or n=3
    elif n&1 = 0 or n%3 = 0 then false
    else
        d := 5;
        comp := false;
        while not comp and d*d <= n do
            if n%d = 0 then comp := true fi;
            d := d + 2;
            if n%d = 0 then comp := true fi;
            d := d + 4
        od;
        not comp
    fi
corp

proc nonrec main() void:
    ulong a, b, c;
    byte n;
    
    a := 1;
    b := 1;
    n := 0;
    while n < 9 do  
        if prime(a) then
            writeln(a);
            n := n + 1
        fi;
        c := a + b;
        a := b;
        b := c
    od
corp
Output:
2
3
5
13
89
233
1597
28657
514229

F#[edit]

// Prime Fibonacci Numbers. Nigel Galloway: January 21st., 2022
seq{yield! [2I;3I]; yield! MathNet.Numerics.Generate.FibonacciSequence()|>Seq.skip 5|>Seq.filter(fun n->n%4I=1I && Open.Numeric.Primes.MillerRabin.IsProbablePrime &n)}|>Seq.take 23|>Seq.iteri(fun n g->printfn "%2d->%A" (n+1) g)
Output:
 1->2
 2->3
 3->5
 4->13
 5->89
 6->233
 7->1597
 8->28657
 9->514229
10->433494437
11->2971215073
12->99194853094755497
13->1066340417491710595814572169
14->19134702400093278081449423917
15->475420437734698220747368027166749382927701417016557193662268716376935476241
16->529892711006095621792039556787784670197112759029534506620905162834769955134424689676262369
17->1387277127804783827114186103186246392258450358171783690079918032136025225954602593712568353
18->3061719992484545030554313848083717208111285432353738497131674799321571238149015933442805665949
19->10597999265301490732599643671505003412515860435409421932560009680142974347195483140293254396195769876129909
20->36684474316080978061473613646275630451100586901195229815270242868417768061193560857904335017879540515228143777781065869
21->96041200618922553823942883360924865026104917411877067816822264789029014378308478864192589084185254331637646183008074629
22->357103560641909860720907774139063454445569926582843306794041997476301071102767570483343563518510007800304195444080518562630900027386498933944619210192856768352683468831754423234217978525765921040747291316681576556861490773135214861782877716560879686368266117365351884926393775431925116896322341130075880287169244980698837941931247516010101631704349963583400361910809925847721300802741705519412306522941202429437928826033885416656967971559902743150263252229456298992263008126719589203430407385228230361628494860172129702271172926469500802342608722006420745586297267929052509059154340968348509580552307148642001438470316229
23->500195636126957292905024512596972806695803345136243348970565288179435361313804956505581782637634612477979679893275103396147348650762007594937510804541145002304302867341006298493404319657382123201158007188252606550806694535329232256851056656372379649097735304781630173812454531781511107460619516018844320335033801984806819067802561370394036732654089838823551603083295670024453477589093119918386566397677610274213837391954591147603054442650326827980781140275941425217172428448698161710841740688042587204161256084914166762549007012713922172748259690566614580062682196606466498102571627683726718483229578044343646737694436406261444368327649097401550241341102704783841619376027737767077127010039900586625841991295111482539736725172169379740443890332234341104310470907449898415522414805210341138063350999730749950920147250683227798780264811215647706542511681027825390882770762662185410080310045261286851842669934849330548237271838345164232560544964315090365421726004108704302854387700053591957

Factor[edit]

Works with: Factor version 0.99 2021-06-02
USING: kernel lists lists.lazy math.primes prettyprint sequences ;

: prime-fib ( -- list )
    { 0 1 } [ [ rest ] [ sum suffix ] bi ] lfrom-by
    [ second ] lmap-lazy [ prime? ] lfilter ;

9 prime-fib ltake [ . ] leach
Output:
2
3
5
13
89
233
1597
28657
514229

Go[edit]

Translation of: C
package main

import "fmt"

func isPrime(n uint64) bool {
    if n < 2 {
        return false
    }
    if n%2 == 0 {
        return n == 2
    }
    if n%3 == 0 {
        return n == 3
    }
    d := uint64(5)
    for d*d <= n {
        if n%d == 0 {
            return false
        }
        d += 2
        if n%d == 0 {
            return false
        }
        d += 4
    }
    return true
}

func main() {
    f1 := uint64(1)
    f2 := f1
    count := 0
    limit := 12 // as far as we can get without using big.Int
    fmt.Printf("The first %d prime Fibonacci numbers are:\n", limit)
    for count < limit {
        f3 := f1 + f2
        if isPrime(f3) {
            fmt.Printf("%d ", f3)
            count++
        }
        f1 = f2
        f2 = f3
    }
    fmt.Println()
}
Output:
The first 12 prime Fibonacci numbers are:
2 3 5 13 89 233 1597 28657 514229 433494437 2971215073 99194853094755497 

J[edit]

Here, we pick a convenient expression and generate fibonacci numbers

fib=: <. 0.5 + (%:5) %~ (2 %~ 1+%:5)^i.63

Then we select the first 9 which are prime:

   9 {. (#~ 1&p:) fib
2 3 5 13 89 233 1597 28657 514229

jq[edit]

Works with jq (*)

Works with gojq, the Go implementation of jq

See Erdős-primes#jq for a suitable definition of `is_prime` as used here.

(*) For unlimited precision integer arithmetic, use gojq.

# Emit an unbounded stream of Fibonacci numbers
def fibonaccis:
  # input: [f(i-2), f(i-1)]
  def fib: (.[0] + .[1]) as $sum
           | if .[2] == 0 then $sum
             else $sum, ([ .[1], $sum ] | fib)
             end;
  [-1, 1] | fib;

"The first 9 prime Fibonacci numbers are:",
limit(9; fibonaccis | select(is_prime))
Output:
The first 9 prime Fibonacci numbers are:
2
3
5
13
89
233
1597
28657
514229

Java[edit]

Uses the PrimeGenerator class from Extensible prime generator#Java.

import java.math.BigInteger;

public class PrimeFibonacciGenerator {
    private PrimeGenerator primeGen = new PrimeGenerator(10000, 200000);
    private BigInteger f0 = BigInteger.ZERO;
    private BigInteger f1 = BigInteger.ONE;
    private int index = 0;

    public static void main(String[] args) {
        PrimeFibonacciGenerator gen = new PrimeFibonacciGenerator();
        long start = System.currentTimeMillis();
        for (int i = 1; i <= 26; ++i) {
            BigInteger f = gen.next();
            System.out.printf("%d: F(%d) = %s\n", i, gen.index - 1, toString(f));
        }
        long finish = System.currentTimeMillis();
        System.out.printf("elapsed time: %g seconds\n", (finish - start)/1000.0);
    }

    private PrimeFibonacciGenerator() {
        for (int i = 0; i < 2; ++i)
            primeGen.nextPrime();
    }

    private BigInteger next() {
        for (;;) {
            if (index > 4) {
                int p = primeGen.nextPrime();
                for (; p > index; ++index)
                    nextFibonacci();
            }
            ++index;
            BigInteger f = nextFibonacci();
            if (f.isProbablePrime(30))
                return f;
        }
    }

    private BigInteger nextFibonacci() {
        BigInteger result = f0;
        BigInteger f = f0.add(f1);
        f0 = f1;
        f1 = f;
        return result;
    }

    private static String toString(BigInteger f) {
        String str = f.toString();
        if (str.length() > 40) {
            StringBuilder s = new StringBuilder(str.substring(0, 20));
            s.append("...");
            s.append(str.substring(str.length() - 20));
            s.append(" (");
            s.append(str.length());
            s.append(" digits)");
            str = s.toString();
        }
        return str;
    }
}
Output:
1: F(3) = 2
2: F(4) = 3
3: F(5) = 5
4: F(7) = 13
5: F(11) = 89
6: F(13) = 233
7: F(17) = 1597
8: F(23) = 28657
9: F(29) = 514229
10: F(43) = 433494437
11: F(47) = 2971215073
12: F(83) = 99194853094755497
13: F(131) = 1066340417491710595814572169
14: F(137) = 19134702400093278081449423917
15: F(359) = 47542043773469822074...62268716376935476241 (75 digits)
16: F(431) = 52989271100609562179...55134424689676262369 (90 digits)
17: F(433) = 13872771278047838271...25954602593712568353 (91 digits)
18: F(449) = 30617199924845450305...49015933442805665949 (94 digits)
19: F(509) = 10597999265301490732...54396195769876129909 (107 digits)
20: F(569) = 36684474316080978061...15228143777781065869 (119 digits)
21: F(571) = 96041200618922553823...31637646183008074629 (119 digits)
22: F(2971) = 35710356064190986072...48642001438470316229 (621 digits)
23: F(4723) = 50019563612695729290...02854387700053591957 (987 digits)
24: F(5387) = 29304412869392580554...82040327194725855833 (1126 digits)
25: F(9311) = 34232086066590238613...37580645424669476289 (1946 digits)
26: F(9677) = 10565977873308861656...95169792504550670357 (2023 digits)
elapsed time: 53.7480 seconds

Julia[edit]

using Lazy
using Primes

fibs = @lazy big"0":big"1":(fibs + drop(1, fibs))

primefibs = @>> fibs filter(isprime)

println(take(9, primefibs)) # List: (2 3 5 13 89 233 1597 28657 514229)

Mathematica/Wolfram Language[edit]

First solution by guessing some upper bound:

Select[Fibonacci /@ Range[100], PrimeQ, 9]
Output:
{2, 3, 5, 13, 89, 233, 1597, 28657, 514229}

Second solution without guessing some upper bound:

list = {};
Do[
  f = Fibonacci[i];
  If[PrimeQ[f],
   AppendTo[list, {i, f}];
   If[Length[list] >= 26, Break[]]
   ]
  ,
  {i, 1, \[Infinity]}
  ];
out=Row[{"F(",#1,") = ",If[IntegerLength[#2]<=10,#2,Row@Catenate[{Take[IntegerDigits[#2],5],{" \[Ellipsis] "},Take[IntegerDigits[#2],-5],{"   (",IntegerLength[#2]," digits)"}}]]}]&@@@list;
TableForm[out,TableHeadings->{Automatic,None}]
Output:
1	F(3) = 2
2	F(4) = 3
3	F(5) = 5
4	F(7) = 13
5	F(11) = 89
6	F(13) = 233
7	F(17) = 1597
8	F(23) = 28657
9	F(29) = 514229
10	F(43) = 433494437
11	F(47) = 2971215073
12	F(83) = 99194 … 55497   (17 digits)
13	F(131) = 10663 … 72169   (28 digits)
14	F(137) = 19134 … 23917   (29 digits)
15	F(359) = 47542 … 76241   (75 digits)
16	F(431) = 52989 … 62369   (90 digits)
17	F(433) = 13872 … 68353   (91 digits)
18	F(449) = 30617 … 65949   (94 digits)
19	F(509) = 10597 … 29909   (107 digits)
20	F(569) = 36684 … 65869   (119 digits)
21	F(571) = 96041 … 74629   (119 digits)
22	F(2971) = 35710 … 16229   (621 digits)
23	F(4723) = 50019 … 91957   (987 digits)
24	F(5387) = 29304 … 55833   (1126 digits)
25	F(9311) = 34232 … 76289   (1946 digits)
26	F(9677) = 10565 … 70357   (2023 digits)

Perl[edit]

#!/usr/bin/perl

use strict; # https://rosettacode.org/wiki/First_9_Prime_Fibonacci_Number
use warnings;
use ntheory qw( is_prime );

my @first;
my $x = my $y = 1;
while( @first < 9 )
  {
  ($x, $y) = ($x + $y, $x);
  is_prime( $x ) and push @first, $x;
  }
print "@first\n";
Output:
2 3 5 13 89 233 1597 28657 514229

Phix[edit]

Library: Phix/online

You can run this online here.

with javascript_semantics
include mpfr.e
integer n = 1, count=0
mpz f = mpz_init()
atom t0 = time(), t1 = time()+1
while count<iff(platform()=JS?21:26) do
    integer fn = iff(n<4?n+2:get_prime(n))
    mpz_fib_ui(f, fn)
    if mpz_prime(f) then
        count += 1
        string e = elapsed(time()-t0)
        printf(1,"%2d: fib(%d) = %s (%s)\n",{count,fn,shorten(mpz_get_str(f)),e})
    elsif platform()!=JS and time()>t1 then
        printf(1,"%d\r",fn)
        t1 = time()+1
    end if
    n += 1
end while
Output:
 1: fib(3) = 2 (0s)
 2: fib(4) = 3 (0.1s)
 3: fib(5) = 5 (0.2s)
 4: fib(7) = 13 (0.2s)
 5: fib(11) = 89 (0.2s)
 6: fib(13) = 233 (0.2s)
 7: fib(17) = 1597 (0.2s)
 8: fib(23) = 28657 (0.2s)
 9: fib(29) = 514229 (0.2s)
10: fib(43) = 433494437 (0.2s)
11: fib(47) = 2971215073 (0.2s)
12: fib(83) = 99194853094755497 (0.2s)
13: fib(131) = 1066340417491710595814572169 (0.2s)
14: fib(137) = 19134702400093278081449423917 (0.2s)
15: fib(359) = 47542043773469822074...62268716376935476241 (75 digits) (0.2s)
16: fib(431) = 52989271100609562179...55134424689676262369 (90 digits) (0.2s)
17: fib(433) = 13872771278047838271...25954602593712568353 (91 digits) (0.2s)
18: fib(449) = 30617199924845450305...49015933442805665949 (94 digits) (0.2s)
19: fib(509) = 10597999265301490732...54396195769876129909 (107 digits) (0.2s)
20: fib(569) = 36684474316080978061...15228143777781065869 (119 digits) (0.2s)
21: fib(571) = 96041200618922553823...31637646183008074629 (119 digits) (0.2s)
22: fib(2971) = 35710356064190986072...48642001438470316229 (621 digits) (2.8s)
23: fib(4723) = 50019563612695729290...02854387700053591957 (987 digits) (14.0s)
24: fib(5387) = 29304412869392580554...82040327194725855833 (1,126 digits) (22.4s)
25: fib(9311) = 34232086066590238613...37580645424669476289 (1,946 digits) (2 minutes and 38s)
26: fib(9677) = 10565977873308861656...95169792504550670357 (2,023 digits) (3 minutes and 3s)

Pike[edit]

Translation of: C
bool isPrime(int n) {
	if (n < 2) {
		return false;
	}
	if (!(n%2)) {
		return n == 2;
	}
	if (!(n%3)) {
		return n == 3;
	}

	int d = 5;
	
	while(d*d <= n) {
		if (!(n%d)) {
			return false;
		}
		d += 2;
		if (!(n%d)) {
			return false;
		}
		d += 4;
	 }
	return true;
}

int main() {
	int limit = 12;

	write("The first " + (string)limit + " prime Fibonacci numbers are:\n");

	int count = 0;
	int f1, f2;
	f1 = f2 = 1;

	while(count < limit) {
		int f3 = f2 + f1;
		if (isPrime(f3)) {
			write((string)f3 + " ");
			count = count + 1;
		}
		f1 = f2;
		f2 = f3;
	}
	write("\n");
	return 0;
}
Output:
The first 12 prime Fibonacci numbers are:
2 3 5 13 89 233 1597 28657 514229 433494437 2971215073 99194853094755497

Python[edit]

print("working...")
print("The firsr 9 Prime Fibonacci numbers:")

num = 0

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

def fib(nr):
	if (nr == 0):
		return 0
	if (nr == 1):
		return 1
	if (nr > 1):
		return fib(nr-1) + fib(nr-2)

for n in range(2,520000):
	x = fib(n)
	if isprime(x):
		num = num + 1
		if (x > 1):
			if (num < 11):
				print(str(x),end=" ")
			else:
				break

print()
print("done...")
Output:
working...
The firsr 9 Prime Fibonacci numbers: 
2 3 5 13 89 233 1597 28657 514229 
done...

Raku[edit]

put ++$ .fmt("%2d: ") ~ $_ for (0, 1, * + * … *).grep( &is-prime )[^20];
Output:
 1: 2
 2: 3
 3: 5
 4: 13
 5: 89
 6: 233
 7: 1597
 8: 28657
 9: 514229
10: 433494437
11: 2971215073
12: 99194853094755497
13: 1066340417491710595814572169
14: 19134702400093278081449423917
15: 475420437734698220747368027166749382927701417016557193662268716376935476241
16: 529892711006095621792039556787784670197112759029534506620905162834769955134424689676262369
17: 1387277127804783827114186103186246392258450358171783690079918032136025225954602593712568353
18: 3061719992484545030554313848083717208111285432353738497131674799321571238149015933442805665949
19: 10597999265301490732599643671505003412515860435409421932560009680142974347195483140293254396195769876129909
20: 36684474316080978061473613646275630451100586901195229815270242868417768061193560857904335017879540515228143777781065869

Ring[edit]

load "stdlibcore.ring"
see "working..." + nl
num = 0

see  "The first 9 Prime Fibonacci numbers: " + nl
for n = 1 to 1000000
     x = fib(n)
     if isprime(x)
        num++
        if num< 10
           ?  "" + x + "  "
        else
           exit
        ok
     ok
next

see "done..." + nl
  
func fib nr
       if nr = 0 return 0 ok
       if nr = 1 return 1 ok 
       if nr > 1 return fib(nr-1) + fib(nr-2) ok
Output:
working...
The first 9 Prime Fibonacci numbers: 
2  3  5  13  89  233  1597  28657  514229  
done...

Rust[edit]

// [dependencies]
// rug = "1.15.0"
// primal = "0.3"

use rug::{Assign, Integer};

fn fibonacci() -> impl std::iter::Iterator<Item = Integer> {
    let mut f0 = Integer::from(0);
    let mut f1 = Integer::from(1);
    std::iter::from_fn(move || {
        let result = Integer::from(&f0);
        let f = Integer::from(&f0 + &f1);
        f0.assign(&f1);
        f1.assign(&f);
        Some(result)
    })
}

fn prime_fibonacci() -> impl std::iter::Iterator<Item = (usize, Integer)> {
    use rug::integer::IsPrime;
    let mut primes = primal::Primes::all().skip(2);
    let mut fib = fibonacci();
    let mut n = 0;
    std::iter::from_fn(move || loop {
        if n > 4 {
            let p = primes.next().unwrap();
            while p > n {
                fib.next();
                n += 1;
            }
        }
        n += 1;
        if let Some(f) = fib.next() {
            if f.is_probably_prime(30) != IsPrime::No {
                return Some((n - 1, f));
            }
        }
    })
}

fn to_string(num: &Integer) -> String {
    let str = num.to_string();
    let len = str.len();
    if len > 40 {
        let mut result = String::from(&str[..20]);
        result.push_str("...");
        result.push_str(&str[len - 20..]);
        result.push_str(" (");
        result.push_str(&len.to_string());
        result.push_str(" digits)");
        return result;
    }
    str
}

fn main() {
    use std::time::Instant;
    let now = Instant::now();
    for (i, (n, f)) in prime_fibonacci().take(26).enumerate() {
        println!("{}: F({}) = {}", i + 1, n, to_string(&f));
    }
    let time = now.elapsed();
    println!("elapsed time: {} milliseconds", time.as_millis());
}
Output:
1: F(3) = 2
2: F(4) = 3
3: F(5) = 5
4: F(7) = 13
5: F(11) = 89
6: F(13) = 233
7: F(17) = 1597
8: F(23) = 28657
9: F(29) = 514229
10: F(43) = 433494437
11: F(47) = 2971215073
12: F(83) = 99194853094755497
13: F(131) = 1066340417491710595814572169
14: F(137) = 19134702400093278081449423917
15: F(359) = 47542043773469822074...62268716376935476241 (75 digits)
16: F(431) = 52989271100609562179...55134424689676262369 (90 digits)
17: F(433) = 13872771278047838271...25954602593712568353 (91 digits)
18: F(449) = 30617199924845450305...49015933442805665949 (94 digits)
19: F(509) = 10597999265301490732...54396195769876129909 (107 digits)
20: F(569) = 36684474316080978061...15228143777781065869 (119 digits)
21: F(571) = 96041200618922553823...31637646183008074629 (119 digits)
22: F(2971) = 35710356064190986072...48642001438470316229 (621 digits)
23: F(4723) = 50019563612695729290...02854387700053591957 (987 digits)
24: F(5387) = 29304412869392580554...82040327194725855833 (1126 digits)
25: F(9311) = 34232086066590238613...37580645424669476289 (1946 digits)
26: F(9677) = 10565977873308861656...95169792504550670357 (2023 digits)
elapsed time: 22642 milliseconds

Sidef[edit]

say 12.by { .fib.is_prime }.map { .fib }
Output:
[2, 3, 5, 13, 89, 233, 1597, 28657, 514229, 433494437, 2971215073, 99194853094755497]

Wren[edit]

Library: Wren-math
import "./math" for Int

var limit = 11 // as far as we can go without using BigInt
System.print("The first %(limit) prime Fibonacci numbers are:")
var count = 0
var f1 = 1
var f2 = 1
while (count < limit) {
    var f3 = f1 + f2
    if (Int.isPrime(f3)) {
        System.write("%(f3) ")
        count = count + 1
    }
    f1 = f2
    f2 = f3
}
System.print()
Output:
The first 11 prime Fibonacci numbers are:
2 3 5 13 89 233 1597 28657 514229 433494437 2971215073 

XPL0[edit]

func IsPrime(N); \Return 'true' if N is prime
int N, I;
[if N <= 2 then return N = 2;
if (N&1) = 0 then return false;
for I:= 3 to sqrt(N) do
    [if rem(N/I) = 0 then return false;
    I:= I+1;
    ];
return true;
];

int F, N, N0, C;
[C:= 0;  N:= 1;  N0:= 1;
loop [F:= N + N0;
     if IsPrime(F) then
        [IntOut(0, F);  ChOut(0, ^ );
        C:= C+1;
        if C >= 9 then quit;
        ];
     N0:= N;
     N:= F;
     ];
]
Output:
2 3 5 13 89 233 1597 28657 514229