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A number n with prime factorization n=product_(i=1)^rp_i^(a_i) is called k-almost prime if it has a sum of exponents sum_(i=1)^(r)a_i=k, i.e., when the prime factor ...

A prime number (or prime integer, often simply called a "prime" for short) is a positive integer p>1 that has no positive integer divisors other than 1 and p itself. More ...

Two integers n and m<n are (alpha,beta)-multiamicable if sigma(m)-m=alphan and sigma(n)-n=betam, where sigma(n) is the divisor function and alpha,beta are positive integers. ...

A Proth number that is prime, i.e., a number of the form N=k·2^n+1 for odd k, n a positive integer, and 2^n>k. Factors of Fermat numbers are of this form as long as they ...

Let a prime number generated by Euler's prime-generating polynomial n^2+n+41 be known as an Euler prime. (Note that such primes are distinct from prime Euler numbers, which ...

In the 1980s, Samuel Yates defined a titanic prime to be a prime number of at least 1000 decimal digits. The smallest titanic prime is 10^(999)+7. As of 1990, more than 1400 ...

A deletable prime is a prime number which has the property that deleting digits one at a time in some order gives a prime at each step. For example, 410256793 is a deletable ...

Given an integer sequence {a_n}_(n=1)^infty, a prime number p is said to be a primitive prime factor of the term a_n if p divides a_n but does not divide any a_m for m<n. It ...

A prime gap of length n is a run of n-1 consecutive composite numbers between two successive primes. Therefore, the difference between two successive primes p_k and p_(k+1) ...

A Belphegor prime (also known as a Beelphegor prime) is a prime Belphegor number, i.e., a palindromic prime of the form 1(0...)666(0...)1. The first few Belphegor primes are ...