Sorry, I didn't mean to make so much of your comparison to RH; I realize you didn't mean to put them in the same league. And I'm quite possibly guilty of describing it as an open problem. But while I do think it is open in a literal sense, I'm not sure if it intrinsically open, so to speak; meaning that it might be a question which is within reach of an expert --- but it might not. (This was more or less the content of MO Scribe's question: is this question just in reach, or just out of reach?) In practice, I don't think the right expert is active on MO, so we may not find out, at least for a while. But it is because of the possibility that it is within reach that I voted to reopen.

Anyway, sorry again to be taking your time with slightly silly comments!

Best wishes,

Matthew

Perhaps I was confused or misremembered: I thought someone somewhere had said it's an open question, which would rule it out as not appropriate for MO. That's all I was saying when I compared it to RH. But anyway, yes, let's see now what happens.

Best,

Todd

I don't think it's quite fair to compare this question to RH. I can imagine that if a hard-core seive expert saw it, they might be able to recognize right away whether it is within reach or not. I just don't think that any such people are reading MO, because if they were, they would have commented on or answered MO Scribe's reformulated question.

Anyway, since it now seems to be open, and we can see what happens!

Best wishes,

Matthew

I happen to know who MO Scribe is, and he is a very strong number theorist. I think that it is best to accept his suggestion that your question is on the cusp of what is known/provable. I have voted to reopen your question, but I don't expect it to be answered, at least not anytime soon. While you can certainly put a bounty on your question, I would be surprised if it will make any difference.

It's not that your question is uninteresting; indeed, as became clear (to me, at least) after MO Scribe's reformulation, it is quite interesting. It's just that it also seems to be quite difficult!

Best wishes,

Matthew Emerton

Other than that, I think (Matthew) Emerton has already explained very nicely what the issues were. It seems to be the case that it is an open problem [hence not suitable for MO -- this site is for questions that the questioner thinks someone will be able to answer, not open problems], but also that it follows from standard conjectures. There were also some issues with how the original question was formulated; MO Scribe presented a more detailed and motivated question which better places it in the matrix of modern-day mathematics. You gave a nod to his formulation, but otherwise the question is about the same as in all the other questions you asked, and so I don't anticipate that the outcome will be any different.