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An odd prime p is called a cluster prime if every even positive integer less than p-2 can be written as a difference of two primes q-q^', where q,q^'<=p. The first 23 odd ...

Two integers are relatively prime if they share no common positive factors (divisors) except 1. Using the notation (m,n) to denote the greatest common divisor, two integers m ...

The largest known prime numbers are Mersenne primes, the largest of these known as of September 2013 bing 2^(57885161)-1, which has a whopping 17425170 decimal digits. As of ...

The primes nearest to the nonnegative integers n=0, 1, 2, ..., assigning ties to the smaller prime, are 2, 2, 2, 3, 3, 5, 5, 7, 7, 7, 11, 11, 11, 13, ... (OEIS A051697). If ...

A p-adic number is an extension of the field of rationals such that congruences modulo powers of a fixed prime p are related to proximity in the so called "p-adic metric." ...

Finch (2001, 2003) defines a k-rough (or k-jagged) number to be positive integer all of whose prime factors are greater than or equal to k. Greene and Knuth define "unusual ...

A "weird number" is a number that is abundant (i.e., the sum of proper divisors is greater than the number) without being pseudoperfect (i.e., no subset of the proper ...

A number n is called wasteful if the number of digits in the prime factorization of n (including powers) uses more digits than the number of digits in n. The first few ...

A Thâbit ibn Kurrah prime, sometimes called a 321-prime, is a Thâbit ibn Kurrah number (i.e., a number of the form 3·2^n-1 for nonnegative integer n) that is prime. The ...

tau(n) is prime for n=63001, 458329, 942841, 966289, 1510441, ... (OEIS A135430). These values are also known as Lehmer-Ramanujan numbers or LR numbers since the first of ...