Timeline for Giuga's Conjecture: Central or Peripheral?
Current License: CC BY-SA 3.0
9 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Feb 16, 2014 at 17:09 | comment | added | The Masked Avenger | I do not consider either Guiga's conjecture or this (possible) extension of Sylvester-Schur to be central: mathoverflow.net/questions/136299/… . However, both are interesting statements about primes. If they Clay Institute puts a large prize out for their solution, that will make them more prominent. It's way too early in the game to say if these or RH are central to what number theory will be two hundred years from now. | |
| Feb 16, 2014 at 9:16 | answer | added | ytreza | timeline score: 3 | |
| Feb 16, 2014 at 9:06 | comment | added | მამუკა ჯიბლაძე | Just playing around: let f(n) = -n/(residue mod n between -n and -1 of the Giuga sum); thus the conjecture is that n is prime iff it is a fixed point of f. Numerical experiments show that if f(n) is a non-prime integer, f(n) is prime. Whereas if it is not integer, iteration still makes sense and gives 1 after few steps. Amusing :) It must be easy to find out which numbers give what. | |
| Feb 16, 2014 at 7:58 | comment | added | Gerry Myerson | Ordinarily, I'd vote to close on the grounds that this is opinion-based. But in this case, I doubt there'll be much difference of opinion. Giuga's conjecture is a favorite of mine, but central? I doubt anyone feels that way. | |
| Feb 16, 2014 at 3:26 | history | edited | Stanley Yao Xiao | CC BY-SA 3.0 |
It's Maynard, not Maynar
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| Feb 16, 2014 at 3:08 | comment | added | KConrad | On the other hand, the Fermat test leads to related ideas (Solovay-Strassen test, Miller-Rabin test) all based on exponentiation in modular arithmetic, which is very feasible. Oh, and to answer your question, Giuga's conjecture is not currently considered central. | |
| Feb 16, 2014 at 3:07 | comment | added | KConrad | Just because a property is (provably or conjecturally) equivalent to something of interest doesn't make it important. In fact, that might be grounds for the result being less useful because it is not a good reformulation of the concept. For instance, compare the Fermat "primality test" (really, compositeness test), which is not an equivalent condition for being prime, with the Wilson "primality test", which is equivalent to being prime: an integer $n > 1$ is prime iff $(n-1)! \equiv -1 \bmod n$. Nobody uses Wilson's criterion to test primality: it is computationally infeasible. | |
| Feb 16, 2014 at 2:41 | history | asked | Joseph O'Rourke | CC BY-SA 3.0 |