Timeline for Effective upper bound on large prime gaps; or, what is the first prime after a googolplex?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 27, 2021 at 14:04 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jun 8, 2014 at 21:21 | comment | added | Terry Tao | Cheng's result unfortunately contains an arithmetic error, but Dudek recovered the result for $e^{e^{33.217}}$ and above: arxiv.org/abs/1401.4233 | |
| Aug 24, 2011 at 6:27 | comment | added | Junkie | There are effective versions of $x^{1-\theta}$ for various $\theta>0$, but the interest in them seems rather low. One explicit example is Cheng's result, which says that $e^{e^{15}}$ suffices to have a prime between $x^3$ and $(x+1)^3$. projecteuclid.org/euclid.rmjm/1268655519 | |
| Nov 1, 2010 at 19:52 | comment | added | Charles | They're trying to find a weak result in the first category (working in polynomial time); I'm trying to find an improvement from the third to the second (from exponential to exponential). They don't need to prove that gaps are small, though that would suffice. So there's a relationship, but it's not that strong. A polynomial-time algorithm for the last bit of pi(x) would solve polymath4 but not my problem, unless it could be shown that it flips in short intervals. | |
| Nov 1, 2010 at 18:17 | comment | added | Péter Komjáth | I think this is the topic of the Polymath4 project. | |
| Nov 1, 2010 at 18:11 | history | asked | Charles | CC BY-SA 2.5 |