Results 11 to 20 of about 7,094,319 (54)

A really trivial proof of the Lucas-Lehmer primality test

, 1993
In the paper [1] Rosen gave a beautiful and elementary proof of the Lucas-Lehmer primality test for Mersenne numbers, i.e. those of the form Mp = 2p - 1.
Bruce, J.W.
core   +6 more sources

Algebraic divisibility sequences over function fields [PDF]

, 2011
In this note we study the existence of primes and of primitive divisors in function field analogues of classical divisibility sequences. Under various hypotheses, we prove that Lucas sequences and elliptic divisibility sequences over function fields ...
Mahe, Valery, Ingram, Patrick, Valéry Mahé, Marco Streng, Streng, T.C., Patrick Ingram, Streng, Marco, Katherine E. Stange, Stange, K.E., Silverman, Joseph H., Mahé, V., Joseph H. Silverman, Silverman, J.H., Ingram, P., Stange, Katherine E.   +14 more
core   +2 more sources

Existence of Primitive Divisors of Lucas and Lehmer Numbers [PDF]

, 1999
We prove that for $n$ > 30, every $n$-th Lucas and Lehmer number has a primitive divisor.
Hanrot, Guillaume, Voutier, Paul, M., Bilu, Yuri   +2 more
core   +5 more sources

Primality Testing

, 2022
Tema ovog rada bit će testovi prostosti. Testove prostosti dijelimo na determinističke i vjerojatnosne. Sukladno tome, rad je podijeljen na dva dijela. Najprije ćemo obraditi probno dijeljenje, Wilsonov teorem, Lucas-Lehmerov test, Pepinov test, AKS test
Moguš, Magdalena
core   +2 more sources

Strengthening the Baillie-PSW primality test

, 2021
Author original manuscript (preprint)In 1980, the first and third authors proposed a probabilistic primality test that has become known as the Baillie-PSW primality test.
Fiori, Andrew, Baillie, Robert, Wagstaff, Samuel S.   +2 more
core   +1 more source

Could, or should, the ancient Greeks have discovered the Lucas-Lehmer test? [PDF]

, 2019
The Lucas-Lehmer (LL) test is the most efficient known for testing the primality of Mersenne numbers, i.e. the integers Ml = 2l − 1, for l ≥ 1. The Mersenne numbers are so-called in honour of the French scholar Marin Mersenne (1588-1648), who in 1644 ...
Granger, Robert
core   +1 more source

Diophantine triples in a Lucas-Lehmer sequence [PDF]

, 2018
In this paper, we define a Lucas-Lehmer type sequence denoted by (Ln)1n=0, and show that there are no integers 0 < a < b < c such that ab + 1, ac + 1 and bc + 1 all are terms of the sequence. Keywords: Diophantine triples, Lucas-Lehmer sequences MSC:
Gueth, Krisztián
core   +1 more source

Primality test via quantum factorization

, 1997
We consider a probabilistic quantum implementation of a variation of the Pocklington-Lehmer N - 1 primality test using Shor's algorithm. O(log3 N log log N log log log N) elementary q-bit operations are required to determine the primality of a number N ...
Chau, HF, Lo, HK
core   +1 more source

UJI PRIMALITAS LUCAS-LEHMER MENGGUNAKAN PROGRAM KOMPUTER [PDF]

, 2010
Untuk mengenali bilangan-bilangan prima yang sangat besar dikembangkanlah beberapa teori uji primalitas. Masing-masing teori yang telah dikembangkan sampai saat ini belum ada yang benar-benar sempurna dalam mengenali bilangan prima.
Kelly, Swandana, Sangadji, Sangadji
core  

Lucas Sequences in Primality Testing

, 2014
Prime or composite? This classification determines whether or not integers can be used in digital security. One such way to begin testing an integers primality is with the Fermat test, which says that if n is a prime number and a is an integer then an-1 ≡
Karl Heimbuck (10081618)
core   +1 more source