Number Theory

    

jA Proof of the Twin Prime Conjecture

Authors: Arthur W. Draut

The traditional definition of the twin prime conjecture is that there is an infinite number of twin primes. The traditional definition of a twin prime is a pair of primes separated by one even number, e.g., 29 and 31. We expand this definition and prove the infinitude of two types of twin primes. Our primary vehicle for proving the twin prime conjecture is a structure that we call Eratos- thenes’ Patterns, which are created by Eratosthenes’ Sieve. First, we describe Eratosthenes’ Sieve, then we describe Eratosthenes’ Patterns, then we give the proof. The essence of our proof is to show that the number of prime twins between pn and p2 n approaches infinity as n approaches infinity.

Comments: 22 Pages.

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Submission history

[v1] 2020-10-01 07:34:53 (removed)
[v2] 2020-10-02 00:53:22
[v3] 2020-10-28 21:28:18
[v4] 2021-06-08 19:36:31

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