A Note on the Decimal Expansion of Reciprocals of Mersenne Primes
The aim of this note is to study, in the realm of Midy's theorem, arithmetic properties of digital blocks in the base-10 expansion of \(1 / M_p\), with \(M_p=2^p-1\) a Mersenne prime. If \(p\) divides the period length \(L\) of \(1/M_p\), one can partition the periodic part into \(p\) blocks, each of length \(\ell\).
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This preprint presents the AiSU Prime Generation Theory as a novel framework for constructing primes through mixed-radix structures, Λ-order control, and convergence analysis.
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