Mathematical analysis reports a record Mersenne prime yielding a 41-million-digit perfect number, highlighting the enduring connection described by the Euclid-Euler theorem.
FINDING: Perfect numbers remain tied to Mersenne primes (Euclid–Euler), with a new record prime \(2¹³⁶²⁷⁹⁸⁴¹-1\) (41,024,320 digits), and a claimed but unverified theorem about primes of form \(6ᵐ⁺¹N-1\). | MATH: Euclid–Euler: even perfect number \(P = 2ᵖ⁻¹(2^p-1)\) iff \(2^p-1\) is Mersenne prime. New prime: \(p=136279841\) (prime), \(M_p = 2¹³⁶²⁷⁹⁸⁴¹-1\) is prime → corresponding perfect number \(2¹³⁶²⁷⁹⁸⁴⁰(2¹³⁶²⁷⁹⁸⁴¹-1)\). Odd perfect numbers: unknown existence; if exist, form \(N = q^α ∏ p_i2β_i\) with \(q ≡ α ≡ 1 4\). Claimed theorem: \(P = 6ᵐ⁺¹N - 1\) prime for \(1 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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Andrew Stewart Caldin (2026) studied this question.