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The previous prime function PP(n) gives the largest prime less than n. The function can be given explicitly as PP(n)=p_(pi(n-1)), where p_i is the ith prime and pi(n) is the ...

Consider a bivariate normal distribution in variables x and y with covariance rho=rho_(11)=<xy>-<x><y> (1) and an arbitrary function g(x,y). Then the expected value of the ...

A short set of data that proves the primality of a number. A certificate can, in general, be checked much more quickly than the time required to generate the certificate. ...

An integer N which is a product of distinct primes and which satisfies 1/N+sum_(p|N)1/p=1 (Butske et al. 1999). The first few are 2, 6, 42, 1806, 47058, ... (OEIS A054377). ...

A prime-distance graph is a distance graph with distance set given by the set of prime numbers.

A symbol used to distinguish one quantity x^' ("x prime") from another related x. Prime marks are most commonly used to denote 1. Transformed coordinates, 2. Conjugate ...

A Banach space X is called prime if each infinite-dimensional complemented subspace of X is isomorphic to X (Lindenstrauss and Tzafriri 1977). Pełczyński (1960) proved that ...

The characteristic function f(n)={1 n is prime; 0 n otherwise (1) of primes has values 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, ... (OEIS A010051) for n=1, 2, ...

The prime distance pd(n) of a nonnegative integer n is the absolute difference between n and the nearest prime. It is therefore true that pd(p)=0 for primes p. The first few ...

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 ...