Towards a deterministic polynomial-time Primality Test

Kayal N., Saxena N.

We examine a primality testing algorithm presented in Primality and Identity Testing via Chinese Remaindering: FOCS 1999 and the related conjecture in Prashant and Rajat: BTP-report 2001. We show that this test is stronger than some of the most popular tests: the Fermat test, the Solovay Strassen test and a strong form of the Fibonacci test. From this, we show the correctness of the algorithm based on a widely believed conjecture, the Extended Riemann Hypothesis. We also show that any n which is accepted by the algorithm must be an odd square-free number. Thus, it is arguably the simplest and yet the strongest test for primality.Based on our computations and results proved in this paper we feel that unlike other tests, this test is very promising as the related conjecture seems provable.