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a heuristic link between divisor counts and prime densities in sequences

Date: Thu., Sept. 18, 2025 Speaker: Benoit Cloitre (independent researcher) Title: A heuristic link between divisor counts and prime densities in sequences Abstract: I introduce a heuristic principle I call "probabilistic continuation" and conjecture a striking asymptotic equivalence: the density of primes in a well-behaved integer sequence appears to match a structural ratio derived from the divisor counts of its terms. The appeal of this conjecture is practical. Determining prime densities usually demands heavy analytic machinery (as in the Prime Number Theorem), whereas the associated divisor ratio is far easier to evaluate. If the conjecture is correct, this ratio could thus provide a simpler proxy for fundamental density measures. I will present the main conjecture, show its consistency with classical results (PNT, PNT in arithmetic progressions, prime distribution in quadratic-residue sequences), and discuss its coherence with Hardy-Littlewood-type conjectures.