Number Theory


Definitive Proof of the Near-Square Prime Conjecture, Landau’s Fourth Problem

Authors: Kenneth A. Watanabe

The Near-Square Prime conjecture, states that there are an infinite number of prime numbers of the form x^2 + 1. In this paper, a function was derived that determines the number of prime numbers of the form x^2 + 1 that are less than n^2 + 1 for large values of n. Then by mathematical induction, it is proven that as the value of n goes to infinity, the function goes to infinity, thus proving the Near-Square Prime conjecture.

Comments: 9 Pages.

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Submission history

[v1] 2019-02-08 09:11:21
[v2] 2019-04-29 08:58:59
[v3] 2019-05-03 15:42:36

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