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The Impact of Mersenne Primes on the Perfection of Numbers

Authors: Saeedi, Samaneh;

The Impact of Mersenne Primes on the Perfection of Numbers

Abstract

Abstract:This research introduces a novel structural perspective on even perfect numbers, moving beyond the classical summation definition toward an "Anatomy of Disintegration." The study proposes that perfection is an absolute settlement between four internal pillars: the Dividend, the Divisor, the Result, and the inherent "Numerical Potential" (Baza'at).By categorizing divisors into three distinct zones—the Body (powers of 2), the Heart (Mersenne Primes), and the Reflection—this paper demonstrates that a perfect number is a balanced geometric system. The "Heart" (Mersenne Prime) acts as a stabilizing anchor that perfectly reflects the Body's potential into the higher divisor range. This symmetry explains the linear stability observed in the distribution of perfect divisors. The findings suggest that mathematical perfection is not a numerical coincidence but a sustainable structural order governed by the Euclid-Mersenne relationship.Keywords: Perfect Numbers,Mersenne Primes, Number Theory, Numerical Potential, Mathematical Symmetry Email:sa.saeedi888@gmail.com

Keywords

Numerical Potential, Mersenne Primes, Number Theory, Perfect Numbers

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green