Strong Pseudoprime
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High Quality Content by WIKIPEDIA articles! In number theory, a strong pseudoprime is a composite number that passes a pseudoprimality test. All primes pass this test, but a small fraction of composites pass as well, making them "false primes". Unlike the Fermat pseudoprimes, for which there exist numbers that are pseudoprimes to all bases (the Carmichael numbers), there are no composites that are strong pseudoprimes to all bases. Formally, a composite number n = d · 2s + 1 with d being odd is called a strong pseudoprime to a relatively prime base a iff one of the following conditions hold: a...
High Quality Content by WIKIPEDIA articles! In number theory, a strong pseudoprime is a composite number that passes a pseudoprimality test. All primes pass this test, but a small fraction of composites pass as well, making them "false primes". Unlike the Fermat pseudoprimes, for which there exist numbers that are pseudoprimes to all bases (the Carmichael numbers), there are no composites that are strong pseudoprimes to all bases. Formally, a composite number n = d · 2s + 1 with d being odd is called a strong pseudoprime to a relatively prime base a iff one of the following conditions hold: a^dequiv 1mod n a^{dcdot 2^r}equiv -1mod nquadmbox{ for some }0leq rleq(s-1) The definition of a strong pseudoprime depends on the base used; different bases have different strong pseudoprimes. It should be noted, however, that Guy uses a definition with only the first condition. Because not all primes pass that condition, this definition of 'strong pseudoprimes' resembles the primes less closely.
