mersenneforum.org > Math a p+1 factoring test for Mp ?
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 2021-01-01, 21:00 #1 bhelmes     Mar 2016 32210 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 Batalov     "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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