Powers of Sierpiński Numbers Base b

Integers ◽  
2010 ◽  
Vol 10 (4) ◽  
Author(s):  
Chris K. Caldwell ◽  
Takao Komatsu
Keyword(s):  
Sierpinski Numbers

AbstractA Sierpiński number is a positive odd integer

scholarly journals An open source software package for primality testing of numbers of the form p2^n+1, with no constraints on the relative sizes of p and 2^n

2018 ◽  
Author(s):  
Tejas R. Rao
Keyword(s):  
Open Source ◽  
Open Source Software ◽  
Software Package ◽  
Primality Testing ◽  
Fermat Number ◽  
Open Source Software Package ◽  
Sierpinski Numbers ◽  
Efficient Software

We develop an efficient software package to test for the primality of p2^n+1, p prime and p>2^n. This aids in the determination of large, non-Sierpinski numbers p, for prime p, and in cryptography. It furthermore uniquely allows for the computation of the smallest n such that p2^n+1 is prime when p is large. We compute primes of this form for the first one million primes p and find four primes of the form above 1000 digits. The software may also be used to test whether p2^n+1 divides a generalized fermat number base 3.

Sierpiński Numbers in Imaginary Quadratic Fields

Integers ◽  
2012 ◽  
Vol 12 (6) ◽  
Author(s):  
Lenny Jones ◽  
Daniel White
Keyword(s):  
Quadratic Fields ◽  
Analogous Problem ◽  
Imaginary Quadratic Fields ◽  
Ring Of Integers ◽  
Sierpinski Numbers

Abstract.In 1960, Sierpiński proved that there exist infinitely many odd positive rational integersIn this article, we investigate the analogous problem in the ring of integers

scholarly journals On powers associated with Sierpiński numbers, Riesel numbers and Polignac's conjecture

2008 ◽  
Vol 128 (7) ◽  
pp. 1916-1940 ◽  
Author(s):  
Michael Filaseta ◽  
Carrie Finch ◽  
Mark Kozek
Keyword(s):  
Sierpinski Numbers ◽  
Riesel Numbers

scholarly journals On Cullen numbers which are both Riesel and Sierpiński numbers

2012 ◽  
Vol 132 (12) ◽  
pp. 2836-2841 ◽  
Author(s):  
Pedro Berrizbeitia ◽  
J.G. Fernandes ◽  
Marcos J. González ◽  
Florian Luca ◽  
V. Janitzio Mejía Huguet
Keyword(s):  
Sierpinski Numbers

scholarly journals An open source software package for primality testing of numbers of the form p2^n+1, with no constraints on the relative sizes of p and 2^n

2018 ◽  
Author(s):  
Tejas R. Rao
Keyword(s):  
Open Source ◽  
Open Source Software ◽  
Software Package ◽  
Primality Testing ◽  
Fermat Number ◽  
Open Source Software Package ◽  
Sierpinski Numbers ◽  
Efficient Software

We develop an efficient software package to test for the primality of p2^n+1, p prime and p>2^n. This aids in the determination of large, non-Sierpinski numbers p, for prime p, and in cryptography. It furthermore uniquely allows for the computation of the smallest n such that p2^n+1 is prime when p is large. We compute primes of this form for the first one million primes p and find four primes of the form above 1000 digits. The software may also be used to test whether p2^n+1 divides a generalized fermat number base 3.

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