Timeline for Are large numbers the sum of two or more large primes? [Hoping for reasonable constants]
Current License: CC BY-SA 3.0
8 events
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| Sep 7, 2011 at 7:25 | history | edited | user2035 |
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| Aug 22, 2011 at 23:44 | comment | added | Junkie | @Fedor Petrov: one cannot write an odd integer as the sum of (say) 10 primes that are all large, as the question preferred. At least one of the primes must be equal to 2, by parity. | |
| Aug 22, 2011 at 14:44 | answer | added | Charles | timeline score: 2 | |
| Aug 22, 2011 at 14:09 | comment | added | Fedor Petrov | What would be possible parity reason? | |
| Aug 22, 2011 at 8:22 | comment | added | Junkie | Ramaré showed in his thesis that at most seven primes suffice. The original result, of such a number of summands, is Schnirelmann's constant. numdam.org/item?id=ASNSP_1995_4_22_4_645_0 He improved Riesel and Vaughan (19 primes). Distinctness, or size considerations, becomes irrelevant fairly quickly, though I do not know an explicit way. The tactic of šnirel’man can also be used, for $p>23$ rather than all primes. The principal technique, is to show sums of two primes have positive density, and extrapolate by summation of these. | |
| Aug 22, 2011 at 6:18 | history | edited | Charles | CC BY-SA 3.0 |
distinct primes
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| Aug 22, 2011 at 6:17 | comment | added | Charles | @Jack Huizenga: Yes, they need to be distinct. Let me edit that in. | |
| Aug 22, 2011 at 6:09 | history | asked | Charles | CC BY-SA 3.0 |