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We describe probabilistic primality tests applicable to integers whose prime factors areall congruent to 1 mod r where r is a positive integer; r = 2 is the Miller{Rabin test.We show that if v rounds of our test do not find n != (r + 1)^2 composite, then n isprime with probability of error less than (2r)^(-v). Applications are given, first to provide a probabilistic primality test applicable to all integers, and second, to give a test for values of cyclotomic polynomials.

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