The Equivalence of Wilson's Theorem and sin(πΩ) = 0

We present a new deterministic criterion for primality based on Wilson's theorem and the sine function. A necessary and sufficient condition for an integer p > 1 to be prime is given by sin(π*Ω) = 0, where Ω = [(p-1)! + 1]/p. This connects elementary number theory with the zeros of a trigonometric function. Keywords: Prime Numbers, Wilson's Theorem, Sine Function, Elementary Number Theory

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-04-26
DOI
https://doi.org/10.5281/zenodo.19777514
Primary Topic
Analytic Number Theory Research
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

The Equivalence of Wilson's Theorem and sin(πΩ) = 0

Sajjad Ali Akbar Tawfiq Sultan
Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
article

The Equivalence of Wilson's Theorem and sin(πΩ) = 0

Sajjad Ali Akbar Tawfiq Sultan
article en

Abstract

We present a new deterministic criterion for primality based on Wilson's theorem and the sine function. A necessary and sufficient condition for an integer p > 1 to be prime is given by sin(π*Ω) = 0, where Ω = [(p-1)! + 1]/p. This connects elementary number theory with the zeros of a trigonometric function. Keywords: Prime Numbers, Wilson's Theorem, Sine Function, Elementary Number Theory

Zenodo (CERN European Organization for Nuclear Research)
Reduced inequalities
Openalex Percentile: Top 4%
Analytic Number Theory Research
DOIOpen Access PDFOpenAlex
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

The Equivalence of Wilson's Theorem and sin(πΩ) = 0 — Sajjad Ali Akbar Tawfiq Sultan · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS