A Fibonacci prime is a Fibonacci number that is prime, a type of integer sequence prime. The first Fibonacci primes are : 2, 3, 5, 13, 89, 233, 1597, 28657, 514229, 433494437, 2971215073, .... Known Fibonacci primes It is not known whether there are infinitely many Fibonacci primes. With the indexing starting with , the first 34 indices n for which Fn is prime are : n = 3, 4, 5, 7, 11, 13, 17, 23, 29, 43, 47, 83, 131, 137, 359, 431, 433, 449, 509, 569, 571, 2971, 4723, 5387, 9311, 9677, 14431, 25561, 30757, 35999, 37511, 50833, 81839, 104911, 130021, 148091. (Note that the actual values Fn rapidly become very large, so, for practicality, only the indices are listed.) In addition to these proven Fibonacci primes, several probable primes have been found: n = 201107, 397379, 433781, 590041, 593689, 604711, 931517, 1049897, 1285607, 1636007, 1803059, 1968721, 2904353, 3244369, 3340367, 4740217, 6530879. Except for the case n = 4, all Fibonacci primes have a prime index, because if a divides b, then also divides (but not every prime index results in a Fibonacci prime). That is to say, the Fibonacci sequence is a divisibility sequence. Fp is prime for 8 of the first 10 primes p; the exceptions are F2 = 1 and F19 = 4181 = 37 × 113. However, Fibonacci primes appear to become rarer as the index increases. Fp is prime for only 26 of the 1,229 primes p below 10,000. The number of prime factors in the Fibonacci numbers with prime index are: 0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 3, 2, 1, 1, 2, 2, 2, 3, 2, 2, 2, 1, 2, 4, 2, 3, 2, 2, 2, 2, 1, 1, 3, 4, 2, 4, 4, 2, 2, 3, 3, 2, 2, 4, 2, 4, 4, 2, 5, 3, 4, 3, 2, 3, 3, 4, 2, 2, 3, 4, 2, 4, 4, 4, 3, 2, 3, 5, 4, 2, 1, ... , the largest known certain Fibonacci prime is F148091, with 30949 digits. It was proved prime by Laurent Facq et al. in September 2021. The largest known probable Fibonacci prime is F6530879. It was found by Ryan Propper in August 2022. It was proved by Nick MacKinnon that the only Fibonacci numbers that are also twin primes are 3, 5, and 13. Divisibility of Fibonacci numbers A prime