Timeline for Faster Solve for Fermat 4n+1 conjecture
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jan 19, 2014 at 1:13 | comment | added | KennyColnago | @DanielLichtblau Thanks! Your PowerMod formulation is compact and much, much faster than the awkward JacobiSymbol equivalent I was using in another non-Cornacchia approach. | |
| Dec 23, 2013 at 22:43 | comment | added | Daniel Lichtblau |
Here is a shorter variant. With[{r = PowerMod[-1, 1/2, p]}, GCD[p, r + I]]. But it's not any faster as far as I can tell.
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| Dec 23, 2013 at 21:44 | comment | added | Mohsen Afshin | I've added new findings | |
| Dec 23, 2013 at 20:16 | comment | added | KennyColnago |
My machine still runs Cornacchia faster than Solve on the larger numbers but, as I said, your timings may vary. The FactorInteger method of @DanielLichtblau should not be dismissed so quickly; it is significantly faster than all so far. Perhaps if you could optimize the Cornacchia algorithm, since its inner workings are visible and not a black box like Solve, then we would all benefit.
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| Dec 23, 2013 at 19:29 | comment | added | Mohsen Afshin | thanks for the solution but the timing in my larger 2K numbers are the same as Solve | |
| Dec 23, 2013 at 18:48 | history | answered | KennyColnago | CC BY-SA 3.0 |