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)
PDF
Publication info
Preprint. Minor revision.
Keywords
Laisant-Beaujeux pseudoprimesfactorialprimality
Contact author(s)
maheswara valluri @ fnu ac fj
History
2019-05-30: last of 2 revisions
2019-02-13: received
See all versions
Short URL
https://ia.cr/2019/125
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2019/125,
      author = {Maheswara Rao Valluri},
      title = {Combinatorial Primality Test},
      howpublished = {Cryptology ePrint Archive, Paper 2019/125},
      year = {2019},
      note = {\url{https://eprint.iacr.org/2019/125}},
      url = {https://eprint.iacr.org/2019/125}
}
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