## Definitive Proof of Legendre's Conjecture

**Authors:** Kenneth A. Watanabe

Legendre's conjecture, states that there is a prime number between n^2 and(n + 1)^2 for every positive integer n. In this paper, an equation was derived that accurately determines the number of prime numbers less than n for large values of n. Then it is proven by induction that there is at least one prime number between n^2 and (n + 1)^2 for all positive integers n thus proving Legendre’s conjecture.

**Comments:** 13 Pages.

**Download:** **PDF**

### Submission history

[v1] 2019-01-29 10:25:44

[v2] 2019-02-11 08:33:18

[v3] 2019-02-13 08:35:02

[v4] 2019-02-26 16:28:14

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