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.
This note, after being uploaded to the arXiv, was reclassified by the arXiv moderators, without any justification being given and without my consent, to the category math.GM. I consider this conduct to be unacceptable, because anything in this category has a reputation as being of highly questionable quality, and thus a reclassification to it may undermine the credibility of a piece of work. The arXiv moderators rejected, once again without any justification being given, my request that the article be removed rather than be placed in math.GM.
Thus, whilst it should not be necessary, I feel called upon firstly to emphasise that the mathematics in this article has been checked to be correct by several (very sharp) people. Secondly, the conjecture does not appear to be known from before. Thirdly, for a fixed k, one can quite easily show, by S-unit equation considerations, that there are at most finitely many n for which the conjecture is false: that is to say, the conjecture holds 'in general'. Thus I consider that the arXiv moderators have overstepped the mark in their handling of the note.
Last updated: 19:29 (GMT+1), 12/02/2018.