composite factorization

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• Composite number — A composite number is a positive integer which has a positive divisor other than one or itself. In other words a composite number is any positive integer greater than one that is not a prime number. So, if n > 0 is an integer and… …   Wikipedia

• Factorization system — In mathematics, it can be shown that every function can be written as the composite of a surjective function followed by an injective function. Factorization systems are a generalization of this situation in category theory.DefinitionA… …   Wikipedia

• Integer factorization — In number theory, integer factorization is the way of breaking down a composite number into smaller non trivial divisors, which when multiplied together equal the original integer.When the numbers are very large, no efficient integer… …   Wikipedia

• Highly composite number — This article is about numbers having many divisors. For numbers factorized only to powers of 2, 3, 5 and 7 (also named 7 smooth numbers), see Smooth number. A highly composite number (HCN) is a positive integer with more divisors than any… …   Wikipedia

• Euler's factorization method — is a method of factorization based upon representing a positive integer N as the sum of two squares in two different ways :N = a^2+ b^2 = c^2+ d^2 (1)Although the algebraic factorization of binomial numbers cannot factor sums of two squares… …   Wikipedia

• Dixon's factorization method — In number theory, Dixon s factorization method (also Dixon s random squares method[1] or Dixon s algorithm) is a general purpose integer factorization algorithm; it is the prototypical factor base method, and the only factor base method for which …   Wikipedia

• Lenstra elliptic curve factorization — The Lenstra elliptic curve factorization or the elliptic curve factorization method (ECM) is a fast, sub exponential running time algorithm for integer factorization which employs elliptic curves. Technically, the ECM is classified as a… …   Wikipedia

• Prime number — Prime redirects here. For other uses, see Prime (disambiguation). A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is… …   Wikipedia

• Quadratic residue — In number theory, an integer q is called a quadratic residue modulo n if it is congruent to a perfect square modulo n; i.e., if there exists an integer x such that: Otherwise, q is called a quadratic nonresidue modulo n. Originally an abstract… …   Wikipedia

• Primality test — A primality test is an algorithm for determining whether an input number is prime. Amongst other fields of mathematics, it is used for cryptography. Unlike integer factorization, primality tests do not generally give prime factors, only stating… …   Wikipedia

• Mersenne prime — Named after Marin Mersenne Publication year 1536[1] Author of publication Regius, H. Number of known terms 47 Conjectured number of terms Infinite …   Wikipedia