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RSA numbers are difficult to-factor composite numbers having exactly two prime factors (i.e., so-called semiprimes) that were listed in the Factoring Challenge of RSA ...

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

For a prime constellation, the Hardy-Littlewood constant for that constellation is the coefficient of the leading term of the (conjectured) asymptotic estimate of its ...

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 ...

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 ...

A Wieferich prime is a prime p which is a solution to the congruence equation 2^(p-1)=1 (mod p^2). (1) Note the similarity of this expression to the special case of Fermat's ...

A Pierpont prime is a prime number of the form p=2^k·3^l+1. The first few Pierpont primes are 2, 3, 5, 7, 13, 17, 19, 37, 73, 97, 109, 163, 193, 257, 433, 487, 577, 769, ... ...

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 primefree sequence is sequence whose terms are never prime. Graham (1964) proved that there exist relatively prime positive integers a and b such that the recurrence ...

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 ...