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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 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) ...

Given a random variable x and a probability density function P(x), if there exists an h>0 such that M(t)=<e^(tx)> (1) for |t|<h, where <y> denotes the expectation value of y, ...

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 ...

Let Gamma be an algebraic curve in a projective space of dimension n, and let p be the prime ideal defining Gamma, and let chi(p,m) be the number of linearly independent ...

A nonzero and noninvertible element a of a ring R which generates a prime ideal. It can also be characterized by the condition that whenever a divides a product in R, a ...

An exponential generating function for the integer sequence a_0, a_1, ... is a function E(x) such that E(x) = sum_(k=0)^(infty)a_k(x^k)/(k!) (1) = ...

A prime circle of order 2n is a free circular permutation of the numbers from 1 to 2n with adjacent pairs summing to a prime. The number of prime circles for n=1, 2, ..., are ...

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 ...

Gaussian primes are Gaussian integers z=a+bi satisfying one of the following properties. 1. If both a and b are nonzero then, a+bi is a Gaussian prime iff a^2+b^2 is an ...