Results 41 to 50 of about 100 (72)
An elliptic curve test for Mersenne primes
, 2005 Let ℓ⩾3 be a prime, and let p=2ℓ-1 be the corresponding Mersenne number. The Lucas–Lehmer test for the primality of p goes as follows. Define the sequence of integers xk by the recursion x0=4,xk=xk-12-2.Then p is a prime if and only if each xk is ...
Gross, Benedict H.
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, 2016 Im August 2002 veröffentlichten Manindra Agrawal, Neeraj Kayal und Nitin Saxena, alle drei Informatiker und Mathematiker am "Indian Institute of Technology Kanpur", den ersten deterministischen Primzahltest mit polynomialer Laufzeit.
Damrau, Milena
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A note on primality testing using Lucas sequences
, 1975 For an odd integer N > 1 N > 1 , thought to be prime, a test is given which uses Lucas sequences and which can establish that any prime divisors of N are ≡ ± 1 \equiv \pm
Michael A. Morrison
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Relaxing the Size Constraint on the Criterion of Proth
, 2019 We add one condition to Proth’s theorem to extend its applicability to N = k2^n + 1 where 2^n > N^(1/3) as opposed to the former constraint of 2^n > k.
Tejas Rao
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Relaxing the Size Constraints on Proth's Criterion
, 2019 We add one condition to Proth’s theorem to extend its applicability to N = k2^n + 1 where 2^n > N^(1/3) as opposed to the former constraint of 2^n > k.
Tejas Rao
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On factorisation, with a suggested new approach
, 1975 This paper gives a brief survey of methods based mainly on Fermat’s Theorem, for testing and establishing primality of large integers. It gives an extension of the Fermat-Lucas-Lehmer Theorems which allows us to establish primality, or to factorise ...
J. C. P. Miller
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Perfect and Mersenne Numbers [PDF]
, 2019 U ovom radu proučavamo Mersenneove i savršene brojeve. Kažemo da je prirodan broj N savršen ako je σ(N) = 2N, gdje je σ(N) suma pravih djelitelja broja N.
Patković, Kristina
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An Algebraic Approach to Test Primality
, 2017 Every 10 minutes, the amount of human generated data expands by more than 10 petabyes. This is equivalent to nearly one third of all literature in all languages from the beginning of recorded history.
Bentz, Brad +4 more
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From perfect numbers to modern primality tests
, 2011 We briefly describe the ideas and results which have led to finding very large prime numbers, and to finding efficient ways of distinguishing prime numbers from composite numbers.
Berrizbeitia, Dr. Pedro
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Primality Tests and Prime Certificate
This note presents a formalisation done in Coq of Lucas-Lehmer test and Pocklington certificate for prime numbers. They both are direct consequences of Fermat little theorem. Fermat little theorem is proved using elementary group theory and in particular
Théry, Laurent
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