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The Generating Functions and Goldbach Conjecture
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Version 1
: Received: 8 March 2024 / Approved: 12 March 2024 / Online: 12 March 2024 (15:43:33 CET)
How to cite: Yang, H. The Generating Functions and Goldbach Conjecture. Preprints 2024, 2024030732. https://doi.org/10.20944/preprints202403.0732.v1 Yang, H. The Generating Functions and Goldbach Conjecture. Preprints 2024, 2024030732. https://doi.org/10.20944/preprints202403.0732.v1
Abstract
It is proved that there exist two odd prime numbers, pi and pj , such that pi + pj = 2r + 2(r ⩾ 2), where pn denote the n-th odd prime number, 1 ⩽ i, j ⩽ n. By the theory of generating functions, we prove that there exist two positive integers, hi and hj , such that hi + hj = r(r ⩾ 2), where hn = (pn − 1)/2，(pn ⩾ 3).Then we complete the proof.
Keywords
generating functions; integer partitions; prime number; the Goldbach conjecture
Subject
Computer Science and Mathematics, Discrete Mathematics and Combinatorics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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