Timeline for Does Zhang's theorem generalize to $3$ or more primes in an interval of fixed length?
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5 events
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| Jun 4, 2013 at 15:28 | comment | added | Johan Andersson | As for the original question, I do not think that anyone has any ideas how to treat more than two primes (I might not be correct of course) | |
| Jun 4, 2013 at 15:27 | comment | added | Johan Andersson | Nick, It sounds like that but I think it might be a misunderstanding. Finding the narrow prime tuples that Tao talks about I think seems related to given a small k0 finding an optimal admissible set H. (that means just finding one such set, not infinitely many) to get as small gap as possible. On the link he gives, such matters are discussed (finding smallest k0 and optimal admissible set). | |
| Jun 4, 2013 at 15:10 | comment | added | Nick Gill | @Noam, Tao's formulation of the polymath proposal suggests to me that (as far as he can see) Zhang's techniques may well yield results for prime tuples, but that some work needs to be done to establish this for certain... | |
| Jun 4, 2013 at 14:56 | comment | added | Noam D. Elkies | Thank you for these links. I already saw Tao's post, but didn't see that it claimed results on prime tuples, only on admissible tuples (which are a key tool in Zhang's proof but aren't themselves known to correspond to prime tuples). The polymath proposal does explicitly target "Finding narrow prime tuples of a given cardinality (or, dually, finding large prime tuples in a given interval)" as part of Part 1 of the project, but doesn't seem to say whether it's known that Zhang's techniques can give such a result. | |
| Jun 4, 2013 at 14:22 | history | answered | Nick Gill | CC BY-SA 3.0 |