Paper 2019/125
Combinatorial Primality Test
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 $4k+3$.
Metadata
- Available format(s)
- -- withdrawn --
- Publication info
- Preprint. MINOR revision.
- Keywords
- Laisant-Beaujeux pseudoprimesfactorialprimality
- Contact author(s)
- maheswara valluri @ fnu ac fj
- History
- 2022-08-24: withdrawn
- 2019-02-13: received
- See all versions
- Short URL
- https://ia.cr/2019/125
- License
-
CC BY