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

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

composites also pass, making them "pseudoprimes". Unlike the Fermat pseudoprimes, for which there exist numbers that are pseudoprimes to all coprime bases (the...

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

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...

property. Carmichael numbers are also called Fermat pseudoprimes or absolute Fermat pseudoprimes. A Carmichael number will pass a Fermat primality test...

which case it is called a strong pseudoprime, and a is a strong liar. Thankfully, no composite number is a strong pseudoprime to all bases at the same time...

restricted Perrin pseudoprimes. There are only nine such numbers below 109. While Perrin pseudoprimes are rare, they overlap with Fermat pseudoprimes. Of the above...

In arithmetic, an odd composite integer n is called an Euler pseudoprime to base a, if a and n are coprime, and a ( n − 1 ) / 2 ≡ ± 1 ( mod n ) {\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...

Euler–Jacobi pseudoprime is also a Fermat pseudoprime and an Euler pseudoprime. There are no numbers which are Euler–Jacobi pseudoprimes to all bases...

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 U (...

part is false: For example, 2341 ≡ 2 (mod 341), but 341 = 11 × 31 is a pseudoprime to base 2. See below. Several proofs of Fermat's little theorem are known...

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...

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...

conditions. While there may be probable primes that are composite (called pseudoprimes), the condition is generally chosen in order to make such exceptions...

Pseudoprimes Carmichael number Catalan pseudoprime Elliptic pseudoprime Euler pseudoprime Euler–Jacobi pseudoprime Fermat pseudoprime Frobenius pseudoprime...

A super-Poulet number is a Poulet number, or pseudoprime to base 2, whose every divisor d divides 2d − 2. For example, 341 is a super-Poulet number: it...

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...

Pseudoprimes Carmichael number Catalan pseudoprime Elliptic pseudoprime Euler pseudoprime Euler–Jacobi pseudoprime Fermat pseudoprime Frobenius pseudoprime...

algorithm Fermat primality test Pseudoprime Carmichael number Euler pseudoprime Euler–Jacobi pseudoprime Fibonacci pseudoprime Probable prime Baillie–PSW primality...

Pseudoprimes Carmichael number Catalan pseudoprime Elliptic pseudoprime Euler pseudoprime Euler–Jacobi pseudoprime Fermat pseudoprime Frobenius pseudoprime...

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 (...

certainly composite. A composite number that passes such a test is called a pseudoprime. In contrast, some other algorithms guarantee that their answer will...

n {\displaystyle n} also have this property. These are the Fibonacci pseudoprimes. L n − L n − 4 {\displaystyle L_{n}-L_{n-4}} is congruent to 0 modulo...

composite. In fact, 341 is the smallest pseudoprime base 2 (see Figure 1 of ). There are only 21853 pseudoprimes base 2 that are less than 2.5×1010 (see...

Pseudoprimes Carmichael number Catalan pseudoprime Elliptic pseudoprime Euler pseudoprime Euler–Jacobi pseudoprime Fermat pseudoprime Frobenius pseudoprime...

Pseudoprimes Carmichael number Catalan pseudoprime Elliptic pseudoprime Euler pseudoprime Euler–Jacobi pseudoprime Fermat pseudoprime Frobenius pseudoprime...

Pseudoprimes Carmichael number Catalan pseudoprime Elliptic pseudoprime Euler pseudoprime Euler–Jacobi pseudoprime Fermat pseudoprime Frobenius pseudoprime...

Pseudoprimes Carmichael number Catalan pseudoprime Elliptic pseudoprime Euler pseudoprime Euler–Jacobi pseudoprime Fermat pseudoprime Frobenius pseudoprime...