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Old 2020-10-06, 14:45   #309
retina
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Quote:
Originally Posted by ATH View Post
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.
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Old 2020-10-06, 15:31   #310
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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.
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Old 2020-10-07, 14:39   #311
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Quote:
Originally Posted by ATH View Post
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?
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Old 2020-10-07, 14:45   #312
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Quote:
Originally Posted by storm5510 View Post
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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