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Legendre showed that there is no rational algebraic function which always gives primes. In 1752, Goldbach showed that no polynomial with integer coefficients can give a prime ...

A symbol used to distinguish one quantity x^' ("x prime") from another related x. Prime marks are most commonly used to denote 1. Transformed coordinates, 2. Conjugate ...

An irreducible algebraic integer which has the property that, if it divides the product of two algebraic integers, then it divides at least one of the factors. 1 and -1 are ...

An arithmetic progression of primes is a set of primes of the form p_1+kd for fixed p_1 and d and consecutive k, i.e., {p_1,p_1+d,p_1+2d,...}. For example, 199, 409, 619, ...

A Banach space X is called prime if each infinite-dimensional complemented subspace of X is isomorphic to X (Lindenstrauss and Tzafriri 1977). Pełczyński (1960) proved that ...

A prime circle of order 2n is a free circular permutation of the numbers from 1 to 2n with adjacent pairs summing to a prime. The number of prime circles for n=1, 2, ..., are ...

The characteristic function f(n)={1 n is prime; 0 n otherwise (1) of primes has values 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, ... (OEIS A010051) for n=1, 2, ...

A prime constellation, also called a prime k-tuple, prime k-tuplet, or prime cluster, is a sequence of k consecutive numbers such that the difference between the first and ...

The prime counting function is the function pi(x) giving the number of primes less than or equal to a given number x (Shanks 1993, p. 15). For example, there are no primes ...

Find two numbers such that x^2=y^2 (mod n). If you know the greatest common divisor of n and x-y, there exists a high probability of determining a prime factor. Taking small ...