Welcome to the resource topic for 2019/125
Title:
Combinatorial Primality Test
Authors: Maheswara Rao Valluri
Abstract:This paper provides proofs of the results of Laisant - Beaujeux: (1) If an integer of the form n=4k+1, k>0 is prime, then \left(\begin{array}{c}n-1\\m\end{array}\right)\equiv1(mod\,n),m=\frac{n-1}{2}, and (2) If an integer of the form n=4k+3, k\geq0 is prime, then \left(\begin{array}{c}n-1\\m\end{array}\right)\equiv-1(mod\,n),m=\frac{n-1}{2}. In addition, the author proposes important conjectures based on the converse of the above theorems which aim to establish primality of n. These conjectures are scrutinized by the given combinatorial primality test algorithm which can also distinguish patterns of prime n whether it is of the form 4k+1 or 4k+3.
ePrint: https://eprint.iacr.org/2019/125
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