A strong pseudoprime is a composite number that passes the Miller–Rabin primality test.
All prime numbers pass this test, but a small fraction of composites also pass, making them "pseudoprimes".
Unlike the Fermat pseudoprimes, for which there exist numbers that are pseudoprimes to all coprime bases (the Carmichael numbers), there are no composites that are strong pseudoprimes to all bases.
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A strongpseudoprime is a composite number that passes the Miller–Rabin primality test. All prime numbers pass this test, but a small fraction of composites...
Lucas pseudoprimes and Fibonacci pseudoprimes are composite integers that pass certain tests which all primes and very few composite numbers pass: in...
an Euler–Jacobi pseudoprime or a strongpseudoprime to every base relatively prime to it so, in theory, either an Euler or a strong probable prime test...
In number theory, the Fermat pseudoprimes make up the most important class of pseudoprimes that come from Fermat's little theorem. Fermat's little theorem...
strong probable prime to base a (see below). For a fixed base a, it is unusual for a composite number to be a probable prime (that is, a pseudoprime)...
In number theory, a Frobenius pseudoprime is a pseudoprime, whose definition was inspired by the quadratic Frobenius test described by Jon Grantham in...
If n is composite and satisfies the formula, then n is a Fibonacci pseudoprime. When m is large – say a 500-bit number – then we can calculate Fm (mod...
These tests are twice as strong as tests based on Fermat's little theorem. Every Euler pseudoprime is also a Fermat pseudoprime. It is not possible to produce...
certainly composite. A composite number that passes such a test is called a pseudoprime. In contrast, some other algorithms guarantee that their answer will...
composite Fermat number is a strongpseudoprime to base 2. This is because all strongpseudoprimes to base 2 are also Fermat pseudoprimes – i.e., 2 F n − 1 ≡ 1...
likely to be a cryptographically strong prime. Note that the criteria for determining if a pseudoprime is a strongpseudoprime is by congruences to powers...
nevertheless superficially impressive; some of them also come under Richard Guy's strong law of small numbers: The only even perfect number of the form n3 + 1 is...
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