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The nth Smarandache-Wellin number is formed from the consecutive number sequence obtained by concatenating of the digits of the first n primes. The first few are 2, 23, 235, ...

Let a and b be nonzero integers such that a^mb^n!=1 (except when m=n=0). Also let T(a,b) be the set of primes p for which p|(a^k-b) for some nonnegative integer k. Then ...

The two functions theta(x) and psi(x) defined below are known as the Chebyshev functions. The function theta(x) is defined by theta(x) = sum_(k=1)^(pi(x))lnp_k (1) = ...

A positive integer n is called a base-b Rhonda number if the product of the base-b digits of n is equal to b times the sum of n's prime factors. These numbers were named by ...

The number two (2) is the second positive integer and the first prime number. It is even, and is the only even prime (the primes other than 2 are called the odd primes). The ...

A pair of primes (p,q) that sum to an even integer 2n=p+q are known as a Goldbach partition (Oliveira e Silva). Letting r(2n) denote the number of Goldbach partitions of 2n ...

A primality test that provides an efficient probabilistic algorithm for determining if a given number is prime. It is based on the properties of strong pseudoprimes. The ...

A prime factorization algorithm.

The symbol p^e∥n means, for p a prime, that p^e|n, but p^(e+1)n.

Two numbers which are relatively prime.