We describe a primality test for with an odd prime p and a positive integer n, which are a particular type of generalized Fermat numbers. We also present special primality criteria for all odd prime numbers p not exceeding 19. All these primality tests run in deterministic polynomial time in the input size log₂M. A special 2pth power reciprocity law is used to deduce our result.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa169-4-1,
author = {Yingpu Deng and Dandan Huang},
title = {Primality test for numbers of the form $(2p)^{2^n}+1$
},
journal = {Acta Arithmetica},
volume = {168},
year = {2015},
pages = {301-317},
zbl = {06456774},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa169-4-1}
}
Yingpu Deng; Dandan Huang. Primality test for numbers of the form $(2p)^{2^n}+1$
. Acta Arithmetica, Tome 168 (2015) pp. 301-317. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa169-4-1/