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2020-10-06, 14:45   #309
retina
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"The unspeakable one"
Jun 2006
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Quote:
 Originally Posted by ATH PRP test = probable prime test, so if positive (zero residue) it is "probably" prime.
Yes, true. But let's be less vague and put a figure on that. We expect something on the order of 99.99...% sureness that it will be prime. The actual figure is unknown, but empirically we see such outcomes.

 2020-10-06, 15:31 #310 ATH Einyen     Dec 2003 Denmark 2,969 Posts Yes, it would be a bigger discovery to find a PRP that was not prime at these sizes than finding the next Mersenne Prime. But I just wanted to stress that PRP test cannot prove primes but Prime95/mprime can with the LL tests.
2020-10-07, 14:39   #311
storm5510
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Aug 2009
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1,621 Posts

Quote:
 Originally Posted by ATH PRP test = probable prime test, so if positive (zero residue) it is "probably" prime. Lucas Lehmer test (LL) proves it is prime if you get a zero residue. Both tests are in Prime95/mprime, but we only need LL test if a PRP test is positive. We switched from LL to PRP tests in the last ~2 years because of the increased (Gerbicz) error checking in PRP tests and now because of the certificates.
There is a little ambiguity in "PRP test is positive." By "positive" you mean a zero residue?

2020-10-07, 14:45   #312
retina
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"The unspeakable one"
Jun 2006
My evil lair

581610 Posts

Quote:
 Originally Posted by storm5510 There is a little ambiguity in "PRP test is positive." By "positive" you mean a zero residue?
PRPs have a different residue, namely 32 (not 0), but essentially, yes, it amounts to the same thing, that a prime is strongly suspected.

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