Number Theory

    

Proof of Legendre Conjecture

Authors: Zhi Li, Hua Li

The Legendre conjecture was proposed by the French mathematician Legendre (1752-1833) andhas not been proved for nearly 200 years. The conjecture is that between any two adjacent perfect square numbers, there is at least one prime number. That is, for any positive integer n, there is a prime number p such that n^2 < p < (n+1)^2.For the distribution of prime number is a distribution of deterministic random, problems related to prime numbers can be studied, analyzed and proved by probability statistics.This paper proves the conjecture by the method of probability and statistics, and proves that the number of prime numbers in the interval from n^2 to (n+1)^2 is similar to the number of prime numbers smaller than the integer n.

Comments: 3 Pages.

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Submission history

[v1] 2022-09-11 02:51:04

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