Williams' P + 1 Algorithm

Williams' P + 1 Algorithm

In computational number theory, Williams' p + 1 algorithm is an integer factorization algorithm, one of the family of algebraic-group factorisation algorithms. It was invented by Hugh C. Williams in 1982.

It works well if the number N to be factored contains one or more prime factors p such that

p + 1

is smooth, i.e. p + 1 contains only small factors. It uses Lucas sequences to perform exponentiation in a quadratic field.

It is analogous to Pollard's p − 1 algorithm.