Sharpening "Primes is in P" for a large family of numbers
Number Theory
2007-05-23 v1
Abstract
We give Deterministic Primality tests for large families of numbers. These tests were inspired in the recent and celebrated Agrawal-Kayal-Saxena (AKS) test. The AKS test has proved polynomial complexity O ((log n)^12) and they expect it to be O ((log n)^6) . Our tests have proved complexity O ((log n)^6). The complexity decreases to O ((log n)^4) as the power of 2 dividing n + 1 or n - 1 increases. On large enough primes, our tests, in their worst case, run at least 2^9 times faster than the AKS test.
Cite
@article{arxiv.math/0211334,
title = {Sharpening "Primes is in P" for a large family of numbers},
author = {Pedro Berrizbeitia},
journal= {arXiv preprint arXiv:math/0211334},
year = {2007}
}