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Old 2021-01-27, 08:14   #1
Nov 2014

1E16 Posts
Default C-PRP residue identical with different factors

Hi, yesterday I did just for fun a P-1 test for the small, already factored number M3331331. This number had one known factor and two C-PRPs for the number divided by the one factor. I found a new factor, did a C-PRP for M3331331 with the two known factors and mprime reported a residue of B786DF1732AE7343.

However, now this residue is also set for the C-PRP test with only 1 factor. This seems to be a bug in Primenet's logic?

Last fiddled with by retina on 2021-01-27 at 09:34 Reason: Remove [bug] tag from title. It's not a bug, it's a feature
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Old 2021-01-27, 08:42   #2
axn's Avatar
Jun 2003

115428 Posts

The residue of the previous tests did not change. The residue produced is same regardless of the factors. P95 merely does another calculation at the end to see if the cofactor is a PRP and report it back if that is the case.
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Old 2021-01-27, 09:29   #3
Nov 2014

2·3·5 Posts

Originally Posted by axn View Post
The residue produced is same regardless of the factors.
Ok, this was not obvious to me. I always assumed it would calculate 3^{\frac{2^n-1}{p}}  \text{ mod } \frac{2^n-1}{p} instead (assuming p is one or more factor). Then the residues would be different.
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