Timeline for Arithmetic progressions without small primes
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 18, 2009 at 17:51 | comment | added | moonface | (This might show up twice by accident, sorry.) Let e > 0. Mindlessly applying the heuristic, the chance f(p) that "there is no prime less than p^{1+e} in the progression" decreases very fast with p; in fact, the sum of f(p) over all p converges, suggesting this event happens only finitely often. For an example of the limitations of such reasoning, see "Primes in short intervals" by H. Maier. | |
| Oct 18, 2009 at 11:47 | comment | added | Harrison Brown | moonface: I'm a bit confused, here. Certainly heuristics given by the PNT would show that for most primes you have p^{1+\epsilon}, but I don't think this rules out the possibility that there are infinitely many primes for which it's not true. (Certainly it doesn't trivially rule out the possibility!) | |
| Oct 18, 2009 at 9:52 | vote | accept | David E Speyer | ||
| Oct 21, 2009 at 3:38 | |||||
| Oct 17, 2009 at 14:16 | history | answered | moonface | CC BY-SA 2.5 |