Number Theory

    

Proof of Fermat's Number Conjecture

Authors: Zhi Li, Hua Li

The natural numbers defined by the sequence F(n) =2^(2^n) + 1, n = 0,1,2,..., are calledFermat numbers. Fermat's conjecture states that there are only finitely many primenumbers in Fermat numbers. It was proposed in 1640 and has not been proved for more than 380 years.The prime number distribution is a deterministic random distribution, so problemsrelated to prime numbers can be studied, analyzed and proved by probability statistics.In this paper, the probability and statistics method is used to prove the conjecture byjudging whether the series converges. Our new conjecture is that there are only five known Fermat primes, namely 3, 5, 17, 257, and 65537.

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[v1] 2022-09-09 17:29:22

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