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.
Cram´ er, On the order of magnitude of the difference be tween consecutive prime numbers, Arkiv f¨ or Mat
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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.