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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If a number has no prime divisors smaller than its root, it kust be prime. For example, the square root of 17 is a little over 4, so if you show 17/2 isn't a whole number, and that 17/3 isn't a whole number, 17 must be prime
According to http://primes.utm.edu , this prime was proven (proof code c82) using the tool Primo which uses Elliptic Curve Primality Proving.
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