2021-01-01, 21:00 | #1 |
Mar 2016
322_{10} Posts |
a p+1 factoring test for Mp ?
A peaceful and pleasent new year 2021,
Is a p+1 factoring test for Mp possible or not ? You could use complex numbers and make a similar factoring test like p-1. In the section math there is no description about it and I see no argument why this should not be possible. Thanks if you spend me some lines. Bernhard |
2021-01-01, 21:30 | #2 |
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
41×229 Posts |
Using Mp and p+1 in one sentence has an unintended consequence that your brain initially assumes that "p" is the same.
You should have phrased you question that (assumed) you mean Williams's p+1 algorithm. Where "p" is actually "f", i.e. the factor to be found. It is possible but will be comparable to ecm. f+1 has the same chances to be smooth as any other number of the same size.* Except you can run many ecm curves, but only one p+1 "curve". _____ *compare: for Mersennes, f-1 contains p, and (f-1)/p has a significantly better chance of being smooth than any sibling of f. |
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