The Equivalence of Wilson's Theorem and sin(πΩ) = 0
Year: 2026
Type: article
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
Author: Sultan, Sajjad Ali Akbar Tawfiq
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7155708002
FWCI:
Cites:
Cited by:
Related to: