Timeline for Efficient ways to count primes satisfying Zhang's theorem
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Oct 26, 2013 at 6:36 | comment | added | Aaron Meyerowitz | It might be more challenging find a prime $P$ with a proof that there are no more before $P+4860.$ Is one known? It certainly seems likely that all the largest Mersenne primes have this property, however we are only able to discover their primality because of their special form. Testing $P+2310$ might be totally beyond out abilities at this point in time. So are there P small enough to let us check $(P,P+4680)$ for primes yet large enough that there is any reasonable chance that there might not be any there to find? | |
| Oct 25, 2013 at 15:28 | comment | added | Gerhard Paseman | Is there a nice writeup of the following problem? Given positive integers k and n, count the number of residue classes c such that gcd(c,n)=gcd(c+k,n)=1? Even if n were restricted to primorials, I would be happy to read such a writeup. Gerhard "Will Look At Small Pieces" Paseman, 2013.10.25 | |
| Oct 25, 2013 at 13:26 | comment | added | Greg Martin | My understanding is that Zhang's proof does not convert into an efficient algorithm. To find large twin primes or close-neighbor primes, the best way is probably to repeatedly choose numbers at random (biasing against having small prime factors) and simply test the two numbers for primality. | |
| Oct 25, 2013 at 7:59 | history | asked | Stanley Yao Xiao | CC BY-SA 3.0 |