Timeline for Is this conjecture on the $n$th record prime gap "true by accident"?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 1, 2018 at 20:17 | vote | accept | Alex | ||
| Jan 5, 2018 at 13:34 | comment | added | reuns | I compared the truth with the random model for the primes ($X_n = 1_{n \text{ is prime}}$ are independent random variables with $P[X_n = 1] = \frac{1}{\log n}$) and the difference doesn't look too high. @Alex | |
| Jan 5, 2018 at 6:13 | comment | added | Alex | Thank you Gerhard. I do agree, we may just know too little, and statements (1) and (2) may be weak approximations to the truth. However, if Cramer's conjecture is true and if another conjecture in arXiv:1709.05508 is also true, namely, if the number of record gaps observed between primes below $x$ is $O(\log x)$, then $O(n^2)$ in (1) might well be the true order of $R(n)$. | |
| Jan 5, 2018 at 5:52 | history | answered | Gerhard Paseman | CC BY-SA 3.0 |