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The sporadic groups are the 26 finite simple groups that do not fit into any of the four infinite families of finite simple groups (i.e., the cyclic groups of prime order, ...

Let p(n) be the first prime which follows a prime gap of n between consecutive primes. Shanks' conjecture holds that p(n)∼exp(sqrt(n)). Wolf conjectures a slightly different ...

z^p-y^p=(z-y)(z-zetay)...(z-zeta^(p-1)y), where zeta=e^(2pii/p) (a de Moivre number) and p is a prime.

A mathematical object invented to solve irreducible congruences of the form F(x)=0 (mod p), where p is prime.

An algorithm which finds the least nonnegative value of sqrt(a (mod p)) for given a and prime p.

A homogeneous ideal defining a projective algebraic variety is unmixed if it has no embedded prime divisors.

The converse of Fermat's little theorem is also known as Lehmer's theorem. It states that, if an integer x is prime to m and x^(m-1)=1 (mod m) and there is no integer e<m-1 ...

Lehmer's formula is a formula for the prime counting function, pi(x) = (1) where |_x_| is the floor function, a = pi(x^(1/4)) (2) b = pi(x^(1/2)) (3) b_i = pi(sqrt(x/p_i)) ...

If 1<=b<a and (a,b)=1 (i.e., a and b are relatively prime), then a^n-b^n has at least one primitive prime factor with the following two possible exceptions: 1. 2^6-1^6. 2. ...

The Lucas-Lehmer test is an efficient deterministic primality test for determining if a Mersenne number M_n is prime. Since it is known that Mersenne numbers can only be ...