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A lucky number of Euler is a number p such that the prime-generating polynomial n^2-n+p is prime for n=1, 2, ..., p-1. Such numbers are related to the imaginary quadratic ...

A modular inverse of an integer b (modulo m) is the integer b^(-1) such that bb^(-1)=1 (mod m). A modular inverse can be computed in the Wolfram Language using PowerMod[b, ...

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 prime factorization algorithm also known as Pollard Monte Carlo factorization method. There are two aspects to the Pollard rho factorization method. The first is the idea ...

Many algorithms have been devised for determining the prime factors of a given number (a process called prime factorization). They vary quite a bit in sophistication and ...

A primitive polynomial is a polynomial that generates all elements of an extension field from a base field. Primitive polynomials are also irreducible polynomials. For any ...

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 prime number theorem shows that the nth prime number p_n has the asymptotic value p_n∼nlnn (1) as n->infty (Havil 2003, p. 182). Rosser's theorem makes this a rigorous ...

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 ...

SNTP(n) is the smallest prime such that p#-1, p#, or p#+1 is divisible by n, where p# is the primorial of p. Ashbacher (1996) shows that SNTP(n) only exists 1. If there are ...