Timeline for a new conjecture about prime maximal gaps
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 23, 2013 at 3:48 | comment | added | Wenlong DU | @quid: When n is not too large, My conjecture gives an approximate value of the prime maximal gap ,which is closed to the actual value. | |
| Jun 22, 2013 at 14:09 | comment | added | user9072 | If you do not even want to claim that the quotient limit exists it is completely unclear why you would ever want to include lower order terms or what is the novelty of your conjecture over existing ones such as Cramér's . Anyway, as I explained the limit is likely at least 1.12. | |
| Jun 21, 2013 at 12:28 | comment | added | Wenlong DU | @quid,@Charles: $\max_{p_{n+1}\leqslant N }(p_{n+1}-p_{n})\approx logN(logN-2loglogN)+2$ do not mean that $$\lim_{n\rightarrow \infty }\frac{\max_{p_{n+1}\leqslant N}(p_{n+1}-p_{n})}{ logN(logN-loglogN)+2}=1$$. Please think it carefully. | |
| Jun 20, 2013 at 20:29 | comment | added | user9072 | ...so one might say that only under this plausible assumption one is lead to conjecture this. Yet the assumption is only plausible and not something conjectured to be true. Anyway, my point to avoid attributing a conjecture was that I thought (perhaps based on a misunderstanding to the extent) that he specifically does not want this to be done. But you see, if the situation is as you say he might have said something like 'I only conjectured inequality not equality' and not what he said. | |
| Jun 20, 2013 at 20:25 | comment | added | user9072 | @Charles: I am not sure. The reason why I am extra careful not to attribute a conjecture to Granville is that recently he pointed out on MO specifically that he did not conjecture a value (contrary to what I claimed) mathoverflow.net/questions/114399/… Now, you say still something else, however from what he said following the link my impression was that there is no conjecture at all, but it isn't very clear either. Yet then the phrase just before the one you quote is 'only' that something is plausible... | |
| Jun 20, 2013 at 19:53 | comment | added | Charles | "Then we are led to conjecture that there are infinitely many primes $p_n$ with $p_{n+1}-p_n>2e^{-\gamma}\log^2p_n,$ contradicting Cramér's conjecture!" (Unexpected irregularities in the distribution of prime numbers, p. 7 in the PDF) | |
| Jun 20, 2013 at 19:44 | comment | added | Charles | What Granville didn't do was conjecture that the lim sup was $2e^{-\gamma}$. He did conjecture that the lim sup was $\ge2e^{-\gamma}$, though. | |
| Jun 20, 2013 at 19:29 | history | answered | user9072 | CC BY-SA 3.0 |