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Old 2021-03-04, 14:21   #19
Dr Sardonicus
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Feb 2017

17DB16 Posts

Originally Posted by charybdis View Post
4. GIMPS now prefers to use PRP rather than LL for primality tests, apart from double-checks of LL results. This is because there is a robust error-checking procedure called the Gerbicz error-check which is almost certain to catch any errors during the test. PRP tests can also be certified, allowing a quick verification that the work was done correctly; this means that a double-check is not needed.
Because of this, apart from double checks on previously LL tested Mp, very few LL tests will be run in future on any Mp, unless it has first tested as a probable prime (i.e. the PRP test fails to prove it composite). If it PRP tests as a probable prime, the result of the LL test will be conclusive. If Mp LL tests as prime, that would be news, because another Mersenne prime would have been found. If an Mp that PRP tests as probable prime then LL tests as composite, that would also be news, because it would be a composite that "fooled" the PRP test.
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