# Category: Pseudoprimes

Euler–Jacobi pseudoprime
In number theory, an odd integer n is called an Euler–Jacobi probable prime (or, more commonly, an Euler probable prime) to base a, if a and n are coprime, and where is the Jacobi symbol. If n is an o
Elliptic pseudoprime
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 with complex multiplication by an order in , havin
Catalan pseudoprime
In mathematics, a Catalan pseudoprime is an odd composite number n satisfying the congruence where Cm denotes the m-th Catalan number. The congruence also holds for every odd prime number n that justi
Lucas pseudoprime
Lucas pseudoprimes and Fibonacci pseudoprimes are composite integers that pass certain tests which all primes and very few composite numbers pass: in this case, criteria relative to some Lucas sequenc
Pseudoprime
A pseudoprime is a probable prime (an integer that shares a property common to all prime numbers) that is not actually prime. Pseudoprimes are classified according to which property of primes they sat
Probable prime
In number theory, a probable prime (PRP) is an integer that satisfies a specific condition that is satisfied by all prime numbers, but which is not satisfied by most composite numbers. Different types
Chinese hypothesis
In number theory, the Chinese hypothesis is a disproven conjecture stating that an integer n is prime if and only if it satisfies the condition that is divisible by n—in other words, that an integer n
Frobenius pseudoprime
In number theory, a Frobenius pseudoprime is a pseudoprime, whose definition was inspired by the quadratic Frobenius test described by Jon Grantham in a 1998 preprint and published in 2000. Frobenius
Fermat pseudoprime
In number theory, the Fermat pseudoprimes make up the most important class of pseudoprimes that come from Fermat's little theorem.
Somer–Lucas pseudoprime
In mathematics, in particular number theory, an odd composite number N is a Somer–Lucas d-pseudoprime (with given d ≥ 1) if there exists a nondegenerate Lucas sequence with the discriminant such that
Strong pseudoprime
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". Unlik
Euler pseudoprime
In arithmetic, an odd composite integer n is called an Euler pseudoprime to base a, if a and n are coprime, and (where mod refers to the modulo operation). The motivation for this definition is the fa
Carmichael number
In number theory, a Carmichael number is a composite number , which in modular arithmetic satisfies the congruence relation: for all integers which are relatively prime to . The relation may also be e