Number Theory

    

A Proof of Twin Prime Conjecture by Using Twin Prime Model Table and Sieve Functions

Authors: Tae Beom Lee

Twin Prime Conjecture(TPC) states that there are infinitely many prime pairs (p, p + 2), where p is prime. But, up to date there is no valid proof of TPC. To prove TPC we devised Twin Prime Model Table(TPMT) and Sieve Functions(SFs). TPMT is a 2-dimensional table representation of all possible twin prime pairs(TPPs). SF is a sine function, f_i (x)=sin πx/p_i , where pi is the ith prime. SFs functionally represent the sieve of Eratosthenes because all zeros of f_i (x) can’t be prime exept the first zero. TPMT explicitly shows the mechanism of how TPPs are found from the possible twin prime pairs. To functionally represent this mechanism we introduced various sinusoidal functions. And by using properties of sinusoidal functions we proved TPC.

Comments: 12 Pages.

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Submission history

[v1] 2021-07-24 21:44:10
[v2] 2023-11-12 23:56:35

Unique-IP document downloads: 342 times

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