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Integer factorization

In mathematics, integer factorization is the decomposition of a positive integer into a product of integers. Every positive integer greater than 1 is either the product of two or more integer factors greater than 1, in which case it is a composite number, or it is not, in which case it is a prime number. For example, 15 is a composite number because 15 =…

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Prime decomposition

Current state of the art

Factoring algorithms

Heuristic running time

Rigorous running time

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Integer factorization

Nodes90
Edges89
Triples41
Avg. degree1.98
Density0.022222
Components1

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Integer factorization

Top relations

related to External links · 21
Integer factorization → Agrawal, Alpern's Integer, Annals, August, Brent, Combinatorics, Computing, Integer Factorisation Algorithms, Mathematics, MathWorld Headline News, Neeraj Kayal, NFS, Nitin Saxena, November, PDFEric, PRIMES, Prospects, Recent Progress, RSA-640 Factored, SIQS
related to Prime decomposition · 10
Integer factorization → AKS, As, By, Fermat's, For, Given, If, Testing, The, While
is a · 1
Integer factorization → decomposition of a positive integer into a product of integers

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Important terminology

algorithm factorization prime integer number time algorithms factors numbers factoring product factor method problem composite example positive factored large running

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Integer factorizationis adecomposition of a positive integer into a product of integers0.90text
RSA public-key encryptioninstance ofThe presumed difficulty of this problem is important for the algorithms used in cryptography0.80text
the RSA digital signatureinstance ofThe presumed difficulty of this problem is important for the algorithms used in cryptography0.80text
Pinstance ofby using NMR techniques on molecules that provide seven qubits.In order to talk about complexity classes0.80text
NPinstance ofby using NMR techniques on molecules that provide seven qubits.In order to talk about complexity classes0.80text
and co-NPinstance ofby using NMR techniques on molecules that provide seven qubits.In order to talk about complexity classes0.80text
the problem has to be stated as a decision problem..mw-parser-output .instance ofby using NMR techniques on molecules that provide seven qubits.In order to talk about complexity classes0.80text
trial divisioninstance ofit is necessary to add a few steps to this algorithm0.80text
and the Jacobi sum test.Expected running timeThe algorithm as stated is a probabilistic algorithm as it makes random choicesinstance ofit is necessary to add a few steps to this algorithm0.80text
and the Jacobi sum testinstance ofit is necessary to add a few steps to this algorithm0.80text
Integer factorizationrelated to External linksSIQS0.60section
Integer factorizationrelated to External linksNFS0.60section

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