The next meeting of the National Seminar on Probability and Statistics will be held on .July 3, 2019 (Wednesday), at 2.00 p.m., in Room 403 of the Institute of Mathematics and Informatics, BAS. A talk on

Probabilistic models for primes

will be delivered by Kevin Ford (University of Illinois at Urbana-Champaign).

Everybody is invited.

Abstract: We introduce a new probabilistic model for primes, which we believe is a better predictor for the behavior of prime in short intervals than the existing models of Cramer and Granville. We also make strong connections between our model, prime k-tuple counts, large gaps and the “square-root sieve”.  In particular, our model makes a prediction about large prime gaps that may contradict the models of Cramer and Granville, depending on the tightness of a certain sieve estimate.