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Pseudoprimes
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A worksheet by Professor Alexandre Borovik defines the two concepts and gives exercises to show the latter is not fooled by the former.
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We know that if a number n successfully passes the Fermat Theorem test described in Lecture 9: bn-1=1 mod n for all coprime bases 0 b n, this does not necessary mean that n is...The first Perrin pseudoprimes and a calculator to test for them.
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Perrin numbers Motivated by a theorem of E. Lucas: If n is prime it divides A(n) exactly, the question whether primality of n follows from n divides A(n) exactly was formulated 1899. So far, they say, nobody...Article in Eric Weisstein's MathWorld.
http://mathworld.wolfram.com/CarmichaelNumber.html
Report by Ashish Kumar Singh and Surendra Kumar Pathak. (PS.GZ)
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BTech Project Abstract WebCaL by Asha Tarachandani and Sumit Gulwani However the major problem with these test has been the existence of Carmichael Numbers. In this report we have tried to extend the Fermat's test to bigger fields and we encountered numbers similar to Carmichael...A pseudoprime type based on symmetric functions. Basic propositions and computational techniques.
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Symmetric Pseudoprimes Theorem states that for any integer c, if p is a prime, then cp c is divisible by p. This is a necessary but not quite sufficient condition for primality, because there are (rare) composites...Articles about many types of pseudoprimes.
http://mathworld.wolfram.com/topics/Pseudoprimes.html