# Miller's test

Should the generalized Riemann hypothesis be proved, the following would gives us a powerful test for primality.

Millers Test:Assume the generalized Riemann hypothesis is true.Ifnis ana-SPRP for all integersawith 1 <a< 2(logn)^{2}, thennis prime.

The constant 2 (which will no doubt be improved) is due to Bach.

**See Also:** Pseudoprime, PRP

**Related pages** (outside of this work)

**References:**

- Bach85
E. Bach,Analytic methods in the analysis and design of number-theoretic algorithms, A.C.M. Distinguished Dissertations The MIT Press, 1985. Cambridge, MA, pp. xiii+48, ISBN 0-262-02219-2.MR 87i:11185

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