Author(s)

Liguo He¹, Gang Zhu²

¹Department of Mathematics, Shenyang University of Technology, Shenyang, China.
²College of Teacher Education, Harbin University, Harbin, China.

The famous strongly binary Goldbach’s conjecture asserts that every even number 2n ≥ 8 can always be expressible as a 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 ≥ 11 is a prime number.

Alternating Group, Element Order Prime Graph, Goldbach’s Conjecture, Centralizer

He, L. and Zhu, G. (2022) Group-Theoretic Remarks on Goldbach’s Conjecture. Advances in Pure Mathematics, 12, 624-637. doi: 10.4236/apm.2022.1211048.