sierpinski numbers
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2018 ◽  
Author(s):  
Tejas R. Rao

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.


2018 ◽  
Author(s):  
Tejas R. Rao

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.


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):  

Integers ◽  
2012 ◽  
Vol 12 (6) ◽  
Author(s):  
Lenny Jones ◽  
Daniel White

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


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

AbstractA Sierpiński number is a positive odd integer


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

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