The Dickson-Mersenne Conjecture: On the Existence of a Mersenne Prime in (2^{n^2}, 16^{n^2})
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We conjecture that for every n >= 1 there exists a Mersenne prime M_p = 2^p - 1 such that 2^{n^2} < M_p < 16^{n^2}. Equivalent to: there is a prime p in (n^2, 4n^2) with 2^p-1 prime. Verified to n=11,674 using known Mersenne primes. Implies infinitude of Mersenne primes. Heuristic support via Lenstra-Pomerance-Wagstaff.
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2026-09-25
