Waldek Hebisch <[email protected]> writes: > Martin Rubey wrote: >> I played a little more with PRIMES, more precisely with >> rabinProvesComposite and prime? >> >> There are at least two things unclear. For example, we have (globally) >> >> rootsMinus1:Set I := empty() >> -- used to check whether we detect too many roots of -1 >> count2Order:Vector NonNegativeInteger := new(1,0) >> -- used to check whether we observe an element of maximal two-order >> >> rootsMinus1 is the set {b^(q 2^(j-1)) : b^(q 2^j) = -1 mod n} >> >> Clearly, when rootsMinus1 contains more than two elements, then n cannot >> be a prime. However, I could not find *any* number such that this >> condition would be triggered in rabinProvesComposite. >> > > AFAIK such cases are extremally rare, it is almost impossible to find > such case via random search and systemtic methods to find them > are quite heavy.
right. I just found Davenports report, and 56897193526942024370326972321 is such a number. Moreover, I found that 1195068768795265792518361315725116351898245581 is considered prime after my modification, which is not true. I'll put these numbers (and any others I can find in Davenport's paper) into the testfile. Martin
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