Primality test for numbers of the form ${\left(2p\right)}^{2^n}+1$

Yingpu Deng, and Dandan Huang. "Primality test for numbers of the form $(2p)^{2^n}+1$." Acta Arithmetica 169.4 (2015): 301-317. <http://eudml.org/doc/278951>.

@article{YingpuDeng2015,
abstract = {We describe a primality test for $M=(2p)^\{2^n\}+1$ 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.},
author = {Yingpu Deng, Dandan Huang},
journal = {Acta Arithmetica},
keywords = {primality test; generalized Fermat numbers; reciprocity law; computational complexity},
language = {eng},
number = {4},
pages = {301-317},
title = {Primality test for numbers of the form $(2p)^\{2^n\}+1$},
url = {http://eudml.org/doc/278951},
volume = {169},
year = {2015},
}

TY - JOUR
AU - Yingpu Deng
AU - Dandan Huang
TI - Primality test for numbers of the form $(2p)^{2^n}+1$
JO - Acta Arithmetica
PY - 2015
VL - 169
IS - 4
SP - 301
EP - 317
AB - We describe a primality test for $M=(2p)^{2^n}+1$ 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.
LA - eng
KW - primality test; generalized Fermat numbers; reciprocity law; computational complexity
UR - http://eudml.org/doc/278951
ER -