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arXiv · 1802.02428

An elementary conjecture which implies the Goldbach conjecture

Richard Williamson
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Abstract

Let $p_{1}$, ..., $p_{k}$ be the first $k$ odd primes in succession. Let $n$ be an even integer such that $n > p_{k}$. We conjecture that if none of $n - p_{1}$, ..., $n - p_{k}$ are prime, then at least one of them has a prime factor which is greater than or equal to $p_{k}$. In this brief note, we observe that Goldbach's conjecture follows from this conjecture.

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Richard Williamson. 2018-02-01. An elementary conjecture which implies the Goldbach conjecture. https://arxiv.org/abs/1802.02428

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