First 9 prime Fibonacci number

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.

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;
end if;
end loop;
end Prime_Fibonacci;
Output:
2
3
5
13
89
233
1597
28657
514229

ALGOL 68

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

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 ;

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.
Output:
2 3 5 13 89 233 1597 28657 514229

AWK

# 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

BASIC256

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

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

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

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

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++

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

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

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.
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.
DIVIDE FIB BY DSOR GIVING DIV-RSLT.
IF DIVISIBLE, MOVE SPACE TO PRIME-FLAG.
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

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

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

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#

// 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

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

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

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

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

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;
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

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

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;
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

#!/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

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

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

from math import sqrt
from time import time

n = 12
start = time()

def prime(x):
if x < 2:
return False
if x == 2 or x == 3:
return True
if x % 2 == 0:
return False
for i in range(3, int(sqrt(x)) + 1, 2):
if x % i == 0:
return False
return True

d = [1, 1]
a, b, = 1, 1
f = []
while len(f) < n:
a, b, = b, a + b
d.append(b)
if prime(b):
f.append(b)
print("fib(%d): %s (%s s)" % (len(f), b, time() - start))
Output:
fib(3): 2 (0.0 s)
fib(4): 3 (0.0 s)
fib(5): 5 (0.0 s)
fib(7): 13 (0.0 s)
fib(11): 89 (0.0 s)
fib(13): 233 (0.0 s)
fib(17): 1597 (0.0 s)
fib(23): 28657 (0.0 s)
fib(29): 514229 (0.0009968280792236328 s)
fib(43): 433494437 (0.0009968280792236328 s)
fib(47): 2971215073 (0.003988504409790039 s)
fib(83): 99194853094755497 (15.122319459915161 s)

Process finished with exit code 0

Quackery

isprime is defined at Primality by trial division#Quackery.

1 1 []
[ dip [ tuck + ]
over isprime iff
[ over join
dup size 9 = ]
else false
until ]
echo 2drop
Output:
[ 2 3 5 13 89 233 1597 28657 514229 ]

Raku

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

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

// [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

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

Wren

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

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