  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.
