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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