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...

composite number is a strong pseudoprime to all bases at the same time (contrary to the Fermat primality test for which Fermat pseudoprimes to all bases exist:...

Lucas pseudoprimes and Fibonacci pseudoprimes are composite integers that pass certain tests which all primes and very few composite numbers pass: in...

Elliptic pseudoprime Euler pseudoprime Euler–Jacobi pseudoprime Fermat pseudoprime Frobenius pseudoprime Lucas pseudoprime Perrin pseudoprime Somer–Lucas...

an Euler–Jacobi pseudoprime or a strong pseudoprime 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)...

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...

In number theory, a Frobenius pseudoprime is a pseudoprime, whose definition was inspired by the quadratic Frobenius test described by Jon Grantham in...

have their own list of pseudoprimes, that is, composite numbers that pass the test. For example, the first ten strong pseudoprimes to base 2 are 2047, 3277...

twice as strong as tests based on Fermat's little theorem. Every Euler–Jacobi pseudoprime is also a Fermat pseudoprime and an Euler pseudoprime. There are...

likely to be a cryptographically strong prime. Note that the criteria for determining if a pseudoprime is a strong pseudoprime is by congruences to powers...

composite Fermat number is a strong pseudoprime to base 2. This is because all strong pseudoprimes to base 2 are also Fermat pseudoprimes – i.e., 2 F n − 1 ≡ 1...

probable prime anyway is at most 1⁄4, in which case p is a strong pseudoprime, and a is a strong liar. Therefore after k non-conclusive random tests, the...

specifically number theory, an odd and composite number N is a Somer–Lucas d-pseudoprime (with given d ≥ 1) if there exists a nondegenerate Lucas sequence U (...

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...

In number theory, a super-Poulet number is a Poulet number, or pseudoprime to base 2, whose every divisor d {\displaystyle d} divides 2 d − 2 {\displaystyle...

In number theory, a pseudoprime is called an elliptic pseudoprime for (E, P), where E is an elliptic curve defined over the field of rational numbers...

In mathematics, a Catalan pseudoprime is an odd composite number n satisfying the congruence ( − 1 ) n − 1 2 ⋅ C n − 1 2 ≡ 2 ( mod n ) , {\displaystyle...

pseudoprime Fermat pseudoprime Frobenius pseudoprime Lucas pseudoprime Lucas–Carmichael number Perrin pseudoprime Somer–Lucas pseudoprime Strong pseudoprime...

contrast, the Lucas pseudoprimes are anti-correlated. Presumably, combining the Perrin and Lucas tests should make a primality test as strong as the reliable...

Mp. All composite divisors of prime-exponent Mersenne numbers are strong pseudoprimes to the base 2. With the exception of 1, a Mersenne number cannot...

pseudoprime Fermat pseudoprime Frobenius pseudoprime Lucas pseudoprime Lucas–Carmichael number Perrin pseudoprime Somer–Lucas pseudoprime Strong pseudoprime...

Solovay–Strassen test does not. This is because 1905 is an Euler pseudoprime base 2 but not a strong pseudoprime base 2 (this is illustrated in Figure 1 of PSW). The...

six primes 4032 – pronic number 4033 – sixth super-Poulet number; strong pseudoprime in base 2 4057 – prime of the form 2p-1 4060 – tetrahedral number...

pseudoprime Fermat pseudoprime Frobenius pseudoprime Lucas pseudoprime Lucas–Carmichael number Perrin pseudoprime Somer–Lucas pseudoprime Strong pseudoprime...

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...

pseudoprime Fermat pseudoprime Frobenius pseudoprime Lucas pseudoprime Lucas–Carmichael number Perrin pseudoprime Somer–Lucas pseudoprime Strong pseudoprime...

composite, 145 is a Fermat pseudoprime in sixteen bases with b < 145. In four of those bases, it is a strong pseudoprime: 1, 12, 17, and 144. the Mertens...

pseudoprime Fermat pseudoprime Frobenius pseudoprime Lucas pseudoprime Lucas–Carmichael number Perrin pseudoprime Somer–Lucas pseudoprime Strong pseudoprime...