4 ms·
Only the simple Fermat tests are vulnerable to Carmichael numbers. The test which is used in practice, Rabin-Miller, is not vulnerable to them. In fact, if you
by pbsd 11y ago
Only the simple Fermat tests are vulnerable to Carmichael numbers. The test which is used in practice, Rabin-Miller, is not vulnerable to them. In fact, if you assume the extended Riemann hypothesis is true, (log n)^2 iterations of Rabin-Miller are sufficient to prove primality.
- schoen 11y agoHow efficient might this be compared to other approaches for searching for Riemann hypothesis counterexamples? Is there a one-to-one relationship between direct Riemann counterexamples and composite numbers that pass (log n)² Rabin-Miller tests?
- pbsd 11y agoI am not familiar with all the ways the GRH can be disproven, but Miller-Rabin doesn't strike me as the most efficient, with its running time of O((log n)^4) for each attempt. I am not sufficiently competent to say whether a GRH counterexample also directly results in a MR counterexample.