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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 primefactor which is greater than or equal to $p_{k}$. In this brief note, weobserve that Goldbach's conjecture follows from this conjecture.

An elementary conjecture which implies the Goldbach conjecture