A generalization of Miller’s primality theorem

Abstract

For any integer r r we show that the notion of ω \omega -prime to base a a introduced by Berrizbeitia and Berry, 2000, leads to a primality test for numbers n n congruent to 1 1 modulo r r , which runs in polynomial time assuming the Extended Riemann Hypothesis (ERH). For r = 2 r = 2 we obtain Miller’s classical result.