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- Primality_certificate abstract "In mathematics and computer science, a primality certificate or primality proof is a succinct, formal proof that a number is prime. Primality certificates allow the primality of a number to be rapidly checked without having to run an expensive or unreliable primality test. By "succinct", we usually mean that we wish for the proof to be at most polynomially larger than the number of digits in the number itself (for example, if the number has b bits, the proof might contain roughly b2 bits).Primality certificates lead directly to proofs that problems such as primality testing and the complement of integer factorization lie in NP, the class of problems verifiable in polynomial time given a solution. These problems already trivially lie in co-NP. This was the first strong evidence that these problems are not NP-complete, since if they were it would imply NP = co-NP, a result widely believed to be false; in fact, this was the first demonstration of a problem in NP intersect co-NP not known (at the time) to be in P.Producing certificates for the complement problem, to establish that a number is composite, is straightforward; it suffices to give a nontrivial divisor. Standard probabilistic primality tests such as the Baillie-PSW primality test, the Fermat primality test, and the Miller-Rabin primality test also produce compositeness certificates in the event where the input is composite, but do not produce certificates for prime inputs.".
- Primality_certificate wikiPageExternalLink Atkin-Goldwasser-Kilian-MorainCertificate.html.
- Primality_certificate wikiPageExternalLink PrattCertificate.html.
- Primality_certificate wikiPageExternalLink PrimalityCertificate.html.
- Primality_certificate wikiPageExternalLink ppp.pdf.
- Primality_certificate wikiPageExternalLink ppp.html.
- Primality_certificate wikiPageExternalLink pratt.pdf.
- Primality_certificate wikiPageID "3691235".
- Primality_certificate wikiPageRevisionID "550571494".
- Primality_certificate hasPhotoCollection Primality_certificate.
- Primality_certificate subject Category:Primality_tests.
- Primality_certificate type Abstraction100002137.
- Primality_certificate type Cognition100023271.
- Primality_certificate type Experiment105798043.
- Primality_certificate type HigherCognitiveProcess105770664.
- Primality_certificate type Inquiry105797597.
- Primality_certificate type PrimalityTests.
- Primality_certificate type ProblemSolving105796750.
- Primality_certificate type Process105701363.
- Primality_certificate type PsychologicalFeature100023100.
- Primality_certificate type Thinking105770926.
- Primality_certificate type Trial105799212.
- Primality_certificate comment "In mathematics and computer science, a primality certificate or primality proof is a succinct, formal proof that a number is prime. Primality certificates allow the primality of a number to be rapidly checked without having to run an expensive or unreliable primality test.".
- Primality_certificate label "Certificado de Primalidade".
- Primality_certificate label "Certyfikat pierwszości".
- Primality_certificate label "Primality certificate".
- Primality_certificate sameAs Certyfikat_pierwszości.
- Primality_certificate sameAs Certificado_de_Primalidade.
- Primality_certificate sameAs m.09vpqh.
- Primality_certificate sameAs Q7243047.
- Primality_certificate sameAs Q7243047.
- Primality_certificate sameAs Primality_certificate.
- Primality_certificate wasDerivedFrom Primality_certificate?oldid=550571494.
- Primality_certificate isPrimaryTopicOf Primality_certificate.