It is named after Ferdinand Georg Frobenius. The test uses the concepts of quadratic polynomials and the Frobenius automorphism. It should not be confused...

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

a Fourier transform acting on quantum bits Quadratic Frobenius test, a primality test QuantiFERON, a test for tuberculosis infection or latent tuberculosis...

Miller–Rabin. The Frobenius test is a generalization of the Lucas probable prime test. The Baillie–PSW primality test is a probabilistic primality test that combines...

Frobenius's theorem (group theory) Frobenius conjecture Frobenius–Schur indicator Perron–Frobenius theorem Quadratic Frobenius test Rouché–Frobenius theorem...

the correctness of the test: as we deal with subgroups of even index, it suffices to assume the validity of GRH for quadratic Dirichlet characters. The...

The Fermat primality test is a probabilistic test to determine whether a number is a probable prime. Fermat's little theorem states that if p is prime...

In mathematics, the Lucas–Lehmer test (LLT) is a primality test for Mersenne numbers. The test was originally developed by Édouard Lucas in 1878 and subsequently...

computed in time O((log n)²) using Jacobi's generalization of the law of quadratic reciprocity. Given an odd number n one can contemplate whether or not...

The AKS primality test (also known as Agrawal–Kayal–Saxena primality test and cyclotomic AKS test) is a deterministic primality-proving algorithm created...

precisely the right order. For Lucas-style tests on a number N, we work in the multiplicative group of a quadratic extension of the integers modulo N; if...

Primality tests AKS APR Baillie–PSW Elliptic curve Pocklington Fermat Lucas Lucas–Lehmer Lucas–Lehmer–Riesel Proth's theorem Pépin's Quadratic Frobenius Solovay–Strassen...

primality test? More unsolved problems in mathematics The Baillie–PSW primality test is a probabilistic or possibly deterministic primality testing algorithm...

is the sieve's key distinction from using trial division to sequentially test each candidate number for divisibility by each prime. Once all the multiples...

Primality tests AKS APR Baillie–PSW Elliptic curve Pocklington Fermat Lucas Lucas–Lehmer Lucas–Lehmer–Riesel Proth's theorem Pépin's Quadratic Frobenius Solovay–Strassen...

{3}{F_{n}}}\right)=-1} from the law of quadratic reciprocity. Because of the sparsity of the Fermat numbers, the Pépin test has only been run eight times (on...

{\displaystyle {\sqrt {kn}},\qquad k\in \mathbb {Z^{+}} } . Since this is a quadratic irrational, the continued fraction must be periodic (unless n is square...

The quadratic sieve algorithm (QS) is an integer factorization algorithm and, in practice, the second-fastest method known (after the general number field...

efficient than the deterministic test, it can be improved both in performance runtime and in accuracy. In practice, a quadratic nonresidue of p is found and...

Pocklington–Lehmer primality test is a primality test devised by Henry Cabourn Pocklington and Derrick Henry Lehmer. The test uses a partial factorization...

In computational number theory, the Adleman–Pomerance–Rumely primality test is an algorithm for determining whether a number is prime. Unlike other, more...

is a nonzero quadratic residue mod p. Note that the quadratic reciprocity law allows one to easily test whether a is a nonzero quadratic residue mod p...

case the Frobenius endomorphism of Z[i]/(p) is the identity. Kummer had already established that if f ∈ {1,2} is the order of the Frobenius automorphism...

reduction is similar to that used for other factoring algorithms, such as the quadratic sieve. A quantum algorithm to solve the order-finding problem. A complete...

was the first multiplication algorithm asymptotically faster than the quadratic "grade school" algorithm. The Toom–Cook algorithm (1963) is a faster generalization...

small factors. It uses Lucas sequences to perform exponentiation in a quadratic field. It is analogous to Pollard's p − 1 algorithm. Choose some integer...

differences the technique of 2-complements and 9-bit masking, which avoids testing the sign of differences), each entry being 16-bit wide (the entry values...

it still wastes almost half of its quadratic computations on non-productive loops that do not pass the modulo tests, so it will not be faster than an equivalent...

In computational number theory, the Lucas test is a primality test for a natural number n; it requires that the prime factors of n − 1 be already known...

methods adapt easily to this application. This can be used for primality testing of large numbers n, for example. Pseudocode A recursive algorithm for ModExp(A...