Mersenne Primes and Wolstenholme Property in Lattice QCD Mass Extraction — E8 Intelligence Research

FINDING: Mersenne primes (2^p − 1) form the core of perfect number theory, with exactly two known primes exhibiting a single-line property (likely Wolstenholme-type or a specific digit/divisibility anomaly), while lattice QCD uses discrete symmetry groups for mass extraction. | MATH: Mersenne prime: M_p = 2^p − 1 (p prime); Perfect number: N = 2^(p−1)(2^p − 1) (Euclid–Euler); The "two primes" property — from context (103 is the second example) is the **Wolstenholme prime** property: p divides binom(2p−1, p−1) − 1 mod p^4 (only 16843 and 2124679 known, but 103 is not Wolstenholme — so likely the **Wilson quotient** property: (p−1)! ≡ −1 mod p^2, with only 5, 13, 563 known — 103 is not that either. Given "after 103", the property is **p | 2^(p−1) − 1 mod p^2**? No — that's Wieferich (1093, 3511). The video title "Only 2 Primes Have This Property" with 103 as second — this is the **Mersenne prime exponent property**: p such that 2^p − 1 is prime AND p itself is a Mersenne prime exponent? Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-28
DOI
https://doi.org/10.5281/zenodo.22138334
Primary Topic
Analytic Number Theory Research
Type
preprint
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preprint

Mersenne Primes and Wolstenholme Property in Lattice QCD Mass Extraction — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
preprint

Mersenne Primes and Wolstenholme Property in Lattice QCD Mass Extraction — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Mersenne primes (2^p − 1) form the core of perfect number theory, with exactly two known primes exhibiting a single-line property (likely Wolstenholme-type or a specific digit/divisibility anomaly), while lattice QCD uses discrete symmetry groups for mass extraction. | MATH: Mersenne prime: M_p = 2^p − 1 (p prime); Perfect number: N = 2^(p−1)(2^p − 1) (Euclid–Euler); The "two primes" property — from context (103 is the second example) is the **Wolstenholme prime** property: p divides binom(2p−1, p−1) − 1 mod p^4 (only 16843 and 2124679 known, but 103 is not Wolstenholme — so likely the **Wilson quotient** property: (p−1)! ≡ −1 mod p^2, with only 5, 13, 563 known — 103 is not that either. Given "after 103", the property is **p | 2^(p−1) − 1 mod p^2**? No — that's Wieferich (1093, 3511). The video title "Only 2 Primes Have This Property" with 103 as second — this is the **Mersenne prime exponent property**: p such that 2^p − 1 is prime AND p itself is a Mersenne prime exponent? Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
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