Prime gaps, probabilistic models and the Hardy-Littlewood conjectures

Combinatorics Seminar
Friday, January 22, 2021 - 3:00pm for 1 hour (actually 50 minutes)
Location (To receive the password, please email Lutz Warnke)
Kevin Ford – The University of Illinois at Urbana-Champaign –
Lutz Warnke

Motivated by a new probabilistic interpretation of the Hardy-Littlewood k-tuples conjectures, we introduce a new probabilistic model of the primes and make a new conjecture about the largest gaps between the primes below x.  Our bound depends on a property of the interval sieve which is not well understood.  We also show that any sequence of integers which satisfies a sufficiently uniform version of the Hardy-Littlewood conjectures must have large gaps of a specific size.  This work is joint with Bill Banks and Terry Tao.