number theory, the Fermat pseudoprimes make up the most important class of pseudoprimes that come from Fermat's little theorem. Fermat's little theorem states...

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

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

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

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...

special case of Fermat's little theorem. However, the "only if" part is false: For example, 2341 ≡ 2 (mod 341), but 341 = 11 × 31 is a pseudoprime to base 2...

1{\pmod {n}}} when n is composite is known as a Fermat liar. In this case n is called Fermat pseudoprime to base a. If we do pick an a such that a n − 1...

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

a Dickson pseudoprime with parameters ( P , Q ) {\displaystyle (P,Q)} , since it is defined by conditions (1) and (3'); a Fermat pseudoprime base | Q |...

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 a definite...

For example, Fermat pseudoprimes to base 2 tend to fall into the residue class 1 (mod m) for many small m, whereas Lucas pseudoprimes tend to fall into...

strong as tests based on Fermat's little theorem. Every Euler–Jacobi pseudoprime is also a Fermat pseudoprime and an Euler pseudoprime. There are no numbers...

pseudoprime to all bases at the same time (contrary to the Fermat primality test for which Fermat pseudoprimes to all bases exist: the Carmichael numbers). However...

only probabilistic, the probability of the Fermat test finding a Fermat pseudoprime that is not prime is vastly lower than the error rate of the Lucas–Lehmer...

Fermat's Last Theorem is a popular science book (1997) by Simon Singh. It tells the story of the search for a proof of Fermat's Last Theorem, first conjectured...

other types of numbers and primes, such as Mersenne and Fermat numbers, specific types of pseudoprimes and some types of numbers generalized from the original...

Fermat number Fermat point Fermat–Weber problem Fermat polygonal number theorem Fermat polynomial Fermat primality test Fermat pseudoprime Fermat quintic threefold...

de Fermat stated (without proof) Fermat's little theorem (later proved by Leibniz and Euler). Fermat also investigated the primality of the Fermat numbers...

n-queens problem for n = 13, decagonal number, centered square number, Fermat pseudoprime 1106 = number of regions into which the plane is divided when drawing...

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...

645 = 3 × 5 × 43, sphenic number, octagonal number, Smith number, Fermat pseudoprime to base 2, Harshad number 646 = 2 × 17 × 19, sphenic number, also...

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

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

Although 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...

into perfect straight-line motion, and vice versa. Sarrus numbers (Fermat pseudoprimes to base 2) are also named after Sarrus, who discovered the first...

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

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...

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...

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...