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For any M, there exists a t^' such that the sequence n^2+t^', where n=1, 2, ... contains at least M primes.

The first Hardy-Littlewood conjecture is called the k-tuple conjecture. It states that the asymptotic number of prime constellations can be computed explicitly. A particular ...

A map x|->x^p where p is a prime.

Sexy primes are pairs of primes of the form (p, p+6), so-named since "sex" is the Latin word for "six.". The first few sexy prime pairs are (5, 11), (7, 13), (11, 17), (13, ...

Each prime factor p_i^(alpha_i) in an integer's prime factorization is called a primary.

A prime factorization algorithm.

Two numbers which are relatively prime.

For N=k·2^n+1 with k odd and 2^n>k, if there exists an integer a such that a^((N-1)/2)=-1 (mod N), then N is prime. A prime of this form is known as a Proth prime.

A test which always identifies prime numbers correctly, but may incorrectly identify a composite number as a prime.

A double Mersenne number is a number of the form M_(M_n)=2^(2^n-1)-1, where M_n is a Mersenne number. The first few double Mersenne numbers are 1, 7, 127, 32767, 2147483647, ...