Improves divisibility results for Bernoulli and other random walks, adds new primality results for Rademacher walks, and gives divisor distribution estimates in the Cramér model.
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Proves a density-1 set where (log n) times the probability that a Cramér model sum S_n is prime is bounded below by 1/sqrt(2 pi e), an asymptotic Gaussian integral formula involving the prime counting function pi(t), and related bounds for quasiprimes and interval lengths tied to Sturm-Liouville.
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Divisibility and primality in random walks
Improves divisibility results for Bernoulli and other random walks, adds new primality results for Rademacher walks, and gives divisor distribution estimates in the Cramér model.
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Critical probabilistic characteristics of the Cram\'er model for primes and arithmetical properties
Proves a density-1 set where (log n) times the probability that a Cramér model sum S_n is prime is bounded below by 1/sqrt(2 pi e), an asymptotic Gaussian integral formula involving the prime counting function pi(t), and related bounds for quasiprimes and interval lengths tied to Sturm-Liouville.