Results 11 to 20 of about 7,411,029 (61)

A simpler alternative to Lucas-Lehmer-Riesel primality test. [PDF]

IACR Cryptol. ePrint Arch., 2023
This paper investigates application of Morrison primality test to numbers of $k \cdot 2^n-1$ form and finds a simple general formula, which is equivalent to Lucas–Lehmer and Lucas–Lehmer–Riesel primality ...
Pavel Atnashev
core   +3 more sources

Lucas-Lehmer Primality Tests for Certain Prime Curios

, 2021
See the abstract in the attached pdf.
Roettger, E. L., Williams, H. C.
openaire   +3 more sources

Cubic reciprocity and generalised Lucas-Lehmer tests for primality of 𝐴.3ⁿ±1 [PDF]

Proceedings of the American Mathematical Society, 1999
Cubic reciprocity is used to derive primality tests analogous to the Lucas-Lehmer test for integers of the form A .3 n
Berrizbeitia, Pedro, Berry, T. G.
openaire   +1 more source

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   +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   +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

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

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., Robert Baillie, Samuel S. Wagstaff, Andrew Fiori   +5 more
core   +1 more source

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   +2 more sources

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