Number Theory

    

A Proof of Mersenne Prime Conjecture

Authors: Zhi Li, Hua Li

The Mersenne Prime Conjecture was proposed in 1644, which refers to whether there areinfinitely many Mersenne primes in a positive integer of the form 2^n- 1. The distribution of prime numbers is a deterministic random distribution, so problems related to prime numbers can be studied, analyzed and proved by probability statistics. This paper proves the conjecture by judging the convergence of the series. At the same time, after the 51st Mersenne prime was proved in 2018, a conservative prediction is made, that is, there are at least 52 Mersenne primes in the Mersenne numbers less than 10^215000000; a more accurate prediction is that there are at least 52 Mersenne numbers in the Mersenne numbers less than10^103000000 prime numbers.

Comments: 4 Pages.

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Submission history

[v1] 2022-09-03 23:25:56

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