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..., which has a positive, but negligible, failure rate, or the [[Baillie–PSW primality test]], which no composites are known to pass. ...user to generate large [[prime numbers]]. [[Primality test|Certifying the primality]] of large numbers (over 100 digits for instance) is significantly harder t ...

...of random numbers, so it is a [[deterministic algorithm|deterministic]] [[primality test]]. It is named after its discoverers, [[Leonard Adleman]], [[Carl Pome ...endrik Willem Lenstra]], commonly referred to as '''APR-CL'''. It can test primality of an integer ''n'' in time: ...

| thesis_title = Riemann's Hypothesis and Tests for Primality | known_for = [[Miller–Rabin primality test]] ...

The '''Fermat primality test''' is a [[randomized algorithm|probabilistic]] test to determine wheth ...'n''>3; ''k'': a parameter that determines the number of times to test for primality ...

...prime testing|primality testing]]. These tests are over twice as strong as tests based on [[Fermat's little theorem]]. ...t2=Strassen |first2=V. |date=1977-03-01 |title=A Fast Monte-Carlo Test for Primality |url=https://epubs.siam.org/doi/10.1137/0206006 |journal=SIAM Journal on Co ...

...algorithm (performing, in expectation, <math>O(\log^2 n)</math> primality tests), is due to [[Adam Tauman Kalai|Adam Kalai]].<ref>{{cite journal ...

...tain a large range of primes; however, to find individual primes, direct [[primality test]]s are more efficient{{citation needed|date=January 2016}}. Furthermor ...[[Miller–Rabin primality test]]. Both the provable and probable primality tests rely on [[modular exponentiation]]. To further reduce the computational cos ...

...Jahren dazu neue Methoden.<br>Williams, J. S. Judd: ''Determination of the primality of N by using prime factors of <math>N^2</math> ± 1.'' In: ''Mathematics o ...ms deals with math history and wrote a book about the history of primality tests. In it, he showed among other things that [[Édouard Lucas]] worked shortly ...

...an unpublished manuscript entitled ''Comparison of probabilistic tests for primality''.<ref>{{cite book|last1=Richard A. Mollin|title=RSA and Public Key Cryptog ...

{{Short description|Probabilistic primality testing algorithm}} ...solved|mathematics|Is there a composite number that passes the Baillie–PSW primality test?}} ...

*Chapter 2 - ''The Price of Primality'' - [[primality test]]s and [[integer factorisation]] ...

...а Римана и проверка простоты чисел» («''Riemann’s Hypothesis and Tests for Primality»''). ...tation.cfm?id=803773&dl=ACM&coll=portal Riemann’s Hypothesis and Tests for Primality]» ...

...S test''') is a [[deterministic algorithm|deterministic]] [[primality test|primality-proving]] [[algorithm]] created and published by [[Manindra Agrawal]], [[Ne AKS is the first primality-proving algorithm to be simultaneously ''general'', ''polynomial-time'', '' ...

...enius pseudoprime to <math>x^3-x-1</math> is also a [[Perrin number#Perrin primality test|restricted Perrin pseudoprime]]. Analogous statements hold for other c ...uthor-link3 = Samuel S. Wagstaff, Jr. |title=Strengthening the Baillie-PSW Primality Test |journal=Mathematics of Computation |date=July 2021 |volume=90 |issue= ...

{{Short description|Methods to check primality}} ...eveloped by [[H. W. Lenstra]] in 1985, and the implications for its use in primality testing (and proving) followed quickly. ...

...ion, cryptoanalysis and security, factorization algorithms and [[primality tests]], [[cryptographic protocols]], key management, electronic payments and dig ...

Fermat's little theorem is the basis for the [[Fermat primality test]] and is one of the fundamental results of [[elementary number theory] ...e [[Lucas primality test]], an important [[primality test]], and Pratt's [[primality certificate]]. ...

|заглавие=Lucasian Criteria for the Primality of ''N'' = ''h''•2^''n''&nbsp;&minus;&nbsp;1 |заглавие=New Primality Criteria and Factorizations of 2^m ± 1 ...

...s inception until 2018, the project relied primarily on the [[Lucas–Lehmer primality test]]<ref>[http://www.mersenne.org/faq.htm#what ''What are Mersenne primes ...18, GIMPS adopted a [[Fermat primality test]] as an alternative option for primality testing,<ref>{{cite web | url=https://www.mersenne.org/various/math.php#luc ...

.... and Carl Pomerance, «[http://www.math.dartmouth.edu/~carlp/aks041411.pdf Primality testing with Gaussian periods] {{Wayback|url=http://www.math.dartmouth.edu/ ...es.apple.com/acg/pdf/aks3.pdf On the implementation of AKS-class primality tests], 2003. ...