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.
Categories: math.GM