Riemann's Hypothesis and tests for primality

  title={Riemann's Hypothesis and tests for primality},
  author={Gary L. Miller},
  journal={Proceedings of the seventh annual ACM symposium on Theory of computing},
  • G. Miller
  • Published 5 May 1975
  • Computer Science, Mathematics
  • Proceedings of the seventh annual ACM symposium on Theory of computing
The purpose of this paper is to present new upper bounds on the complexity of algorithms for testing the primality of a number. The first upper bound is 0(n1/7); it improves the previously best known bound of 0(n1/4) due to Pollard [11]. The second upper bound is dependent on the Extended Riemann Hypothesis (ERH): assuming ERH, we produce an algorithm which tests primality and runs in time 0((log n)4) steps. Thus we show that primality is testable in time a polynomial in the length of the… Expand
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