Frobenius primality test. See details in arXiv:1807.07249 [math.NT]: Evaluation of the Effectiveness of the Frobenius Primality Test.
(c)Sergei Khashin [email protected]
This is a probabilistic method.
The numbers on which it is wrong are called Frobenius pseudoprimes (FPP). Have been proved:
a) There are no FPP < 2^64.
b) There are many other limitations on FPP.
c) There is no known FPP at all.
There is a hypothesis that FPP does not exist at all.
see also: http://arxiv.org/abs/1807.07249