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
Keyword(s):
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 ◽
2015 ◽
Vol 68
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pp. 166-174
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2014 ◽
Vol 10
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pp. 641-652
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2017 ◽
Vol 23
(S1)
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pp. 214-215
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Keyword(s):
2012 ◽
Vol 24
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pp. 84-102
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Keyword(s):
2006 ◽
Vol 174
(5)
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pp. 422-429
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