Results 11 to 20 of about 463 (134)

On Primality testing [PDF]

, 2000
In this study, prime numbers and primality, which IS one of the most important topics in number theory is analyzed.Subject of primality of a number has been the focus of many scientific studies and several different theories has been developed for many years. Based on these theorems, primality of large numbers has been investigated.
Tepeli, Murat
openaire   +3 more sources

Direct product primality testing of graphs is GI-hard [PDF]

, 2021
We investigate the computational complexity of the graph primality testing problem with respect to the direct product (also known as Kronecker, cardinal or tensor product). In [1] Imrich proves that both primality testing and a unique prime factorization
Calderoni, Luca, Marzolla, Moreno, Margara, Luciano   +2 more
core   +1 more source

Primality testing and Jacobi sums [PDF]

, 1984
We present a theoretically and algorithmically simplified version of a primality testing algorithm that was recently invented by Adleman and Rumely. The new algorithm performs well in practice.
Cohen, H., H. Cohen, Lenstra, H.W., H. W. Lenstra   +3 more
core   +1 more source

Characterization of prime and composite numbers using the notion of successive sum of integers and the consequence in primality testing [PDF]

Notes on Number Theory and Discrete Mathematics
In this paper, we give a characterization of primes and composite natural numbers using the notion of the sum of successive natural numbers. We prove essentially that an odd natural number N≥3 is prime if and only if the unique decomposition of N as a ...
Fateh Mustapha Dehmeche, Douadi Mihoubi, Lahcene Ladjelat   +2 more
doaj   +1 more source

METHOD OF TESTING LARGE NUMBERS FOR PRIMALITY

Сучасні інформаційні системи
The current stage of scientific and technological development entails ensuring information security across all domains of human activity. Confidential data and wireless channels of remote control systems are particularly sensitive to various types of ...
Vladimir Pevnev , Oles Yudin , Peter Sedlaček , Nina Kuchuk   +3 more
doaj   +1 more source

Analytic Proofs of Baseline Primality Conjecture for Special Cases

, 2019
In this set of three companion manuscripts/articles, we unveil our new results on primality testing and reveal new primality testing algorithms enabled by those results.
Sherman, Alan T., Phatak, Dhananjay, Houston, Steven D., Henry, Andrew   +3 more
core   +1 more source

A Performant, Misuse-Resistant API for Primality Testing [PDF]

, 2020
Primality testing is a basic cryptographic task. But developers today are faced with complex APIs for primality testing, along with documentation that fails to clearly state the reliability of the tests being performed.
Jake Massimo, Paterson, Kenneth G., Kenneth G. Paterson, Kenneth G. Paterson, Massimo, Jake   +4 more
core   +1 more source

Primality Tests and Prime Certificate

CoRR, 2022
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 Lagrange theorem.
Laurent Théry, Sophia Antipolis
openaire   +2 more sources

Primality test (When an integer test is enough for primality)

, 2021
A programatic way to test for primes using only an integer test for a specific prime series.
openaire   +1 more source

ON A NEW CLASS OF SMARANDACHE PRIME NUMBERS [PDF]

, 2005
The purpose of this note is to report on the discovery of some new prime numbers that were built from factorials, the Smarandache Consecutive Sequence, and the Smarandache Reverse ...
Earls, Jason
core   +1 more source