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arXiv · 1902.00841

Group-theoretic remarks on Goldbach's conjecture

Liguo He·Xianyu Hu
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Abstract

The famous strongly binary Goldbach's conjecture asserts that every even number $2n \geq 8$ can always be expressible as the sum of two distinct odd prime numbers. We use a new approach to dealing with this conjecture. Specifically, we apply the element order prime graphs of alternating groups of degrees $2n$ and $2n-1$ to characterize this conjecture, and present its six group-theoretic versions; and further prove that this conjecture is true for $p+1$ and $p-1$ whenever $p \geq 11$ is a prime number.

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Liguo He, Xianyu Hu. 2019-02-03. Group-theoretic remarks on Goldbach's conjecture. https://arxiv.org/abs/1902.00841

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