An elementary conjecture which implies the Goldbach conjecture

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.

2 pages