Number Theory and Primality

In 1975, Vaughan Pratt showed that there existed a certificate for primality that was checkable in polynomial time, and thus that PRIMES was in NP

The BBP formula gives rise to a spigot algorithm for computing the nth base-16 (hexadecimal) digit of π

the special number field sieve (SNFS) is a special-purpose integer factorization algorithm.

is a general-purpose integer factorization algorithm; it is the prototypical factor base method.

is a number theoretic integer factorization algorithm, invented by John Pollard in 1974

is a probabilistic or possibly deterministic primality testing algorithm that determines whether a number is composite or is a probable prime.

the sieve of Sundaram is a variant of the sieve of Eratosthenes, a simple deterministic algorithm for finding all the prime numbers up to a specified integer.

is a probabilistic primality test to determine if a number is composite or probably prime.

is a primality test for Mersenne numbers

is a primality test, which can be used to determine whether a Fermat number is prime

is an algorithm for determining whether a number is prime

is an integer factorization algorithm

Fermat's factorization method tries to exploit this fact by guessing the first square

The oldest and simplest method, known since antiquity as long multiplication or grade-school multiplication, consists of multiplying every digit in the first number by every digit in the second and adding the results.

Lattice multiplication, also known as the Italian method, Chinese method, Chinese lattice, gelosia multiplication, sieve multiplication, shabakh, diagonally or Venetian squares, is a method of multiplication that uses a lattice to multiply two multi-digit numbers.

is a probabilistic test to determine whether a number is a probable prime

the Lucas test is a primality test for a natural number n

is an algorithm that computes the greatest common divisor (GCD) of two nonnegative integers

multiplies two signed binary numbers in two

is a technique for factoring a number

In mathematics, the Lucas-Lehmer-Riesel test is a primality test for numbers of the form N = k · 2n − 1 with odd k < 2n.

In computational number theory, Williams's p + 1 algorithm is an integer factorization algorithm

are among the quickest and most widely used methods in primality proving

short division is a division algorithm which breaks down a division problem into a series of easier steps

In arithmetic geometry, the Cox-Zucker machine is an algorithm introduced by David A. Cox and Steven Zucker for studying elliptic surfaces.

integer factorization algorithms

In number theory, the integer square root