This is the largest known Fibonacci number that's also prime, which is 21925 digits long and was proved prime by Mathew Steine and Bouk de Water in 2015.pic.twitter.com/eu1t2WEvDZ
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Probably yes. Not proved yet. However, it was proved that the only Fibonacci numbers that are also members of the set of twin primes are 3, 5, and 13. A twin prime is a prime number that is either 2 less or 2 more than another prime number. E.g. (11, 13)
Note this only works in one direction. It may be that n is prime but F_n is composite. For example F_19 =4182=37*113.
Ugh, that should be 4181 not 4182.
We do know that some of the prime-indexed (and only prime-indexed) Fib numbers are primes Since there are infinitely many primes, there are infinitely many prime-indexes Fib numbers which indicates there should be infinitely many prime Fib numbers, but we don’t know for sure
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