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Primality certificate

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. "Succinct" usually means that the proof should be at most polynomially larger than…

Science, Atkin–Goldwasser–Kilian–Morain certificates & Pratt certificates

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Overview

Pratt certificates

Atkin–Goldwasser–Kilian–Morain certificates

Pocklington-based certificates

Gerbicz-based certificate

AKS certificate ("PRIMES is in P")

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Primality certificate

Nodes58
Edges57
Triples35
Avg. degree1.97
Density0.034483
Components1

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Primality certificate

Top relations

related to External links · 13
Primality certificate → Atkin-Goldwasser-Kilian-Morain CertificateThe Prime Glossary, Certificate, Computer Science, Concordia University, Department, Lecture, Mathworld, PDF, Pratt CertificateMathworld, Pratt's Primality Proofs, Primality CertificateMathworld, PrimalityVašek Chvátal, Rutgers University
related to Pratt certificates · 6
Primality certificate → Fermat's, It, Lucas, Pratt, The, Vaughan Pratt
related to Pocklington-based certificates · 5
Primality certificate → Pocklington, Pocklington's, Pocklington-based, Provable, While
related to Pocklington primality certificate · 3
Primality certificate → P-1, Pocklington, The

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Important terminology

displaystyle prime primality certificate certificates number log time test used primes known mod proof numbers pratt scheme verify exponentiation using

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
primality testinginstance ofPrimality certificates lead directly to proofs that problems0.80text
the complement of integer factorization lie in NPinstance ofPrimality certificates lead directly to proofs that problems0.80text
the class of problems verifiable in polynomial time given a solutioninstance ofPrimality certificates lead directly to proofs that problems0.80text
the Baillieinstance ofStandard probabilistic primality tests0.80text
Fermat primesinstance ofThis is simple for some special numbers0.80text
but currently much more difficult than simple primality testing for large primes of general forminstance ofThis is simple for some special numbers0.80text
generating provably valid RSA keys.Time spent on generating an ECPP certificate is not boundedinstance ofan application that is important in cryptography applications0.80text
but a heuristic argument gives Õinstance ofan application that is important in cryptography applications0.80text
Primality certificaterelated to External linksMathworld0.60section
Primality certificaterelated to External linksPrimality CertificateMathworld0.60section
Primality certificaterelated to External linksPratt CertificateMathworld0.60section
Primality certificaterelated to External linksAtkin-Goldwasser-Kilian-Morain CertificateThe Prime Glossary0.60section

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