### Prime gaps, probabilistic models and the Hardy-Littlewood conjectures

- Series
- Combinatorics Seminar
- Time
- Friday, January 22, 2021 - 15:00 for 1 hour (actually 50 minutes)
- Location
- https://bluejeans.com/751242993/PASSWORD (To receive the password, please email Lutz Warnke)
- Speaker
- Kevin Ford – The University of Illinois at Urbana-Champaign

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.