Sharpening "Primes is in P" for a large family of numbers

2002/11/20 by Pedro Berrizbeitia, Berrizbeitia, Pedro
Mathematics · #11A51 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11A51

paper · pdf · doi:10.48550/arxiv.math/0211334

arxiv created 2002/11/20 · arxiv updated 2009/11/30

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 2⁹ times faster than the AKS test.

Related

• Deterministic Primality Testing - understanding the AKS algorithm
• Four primality testing algorithms
• A primality test for Kpⁿ+1 numbers
• Primality Proving via One Round in ECPP and One Iteration in AKS
• Primality tests for specific classes of N=k⋅ 2^m ± 1