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Title: Large prime gaps and probabilistic models
Abstract We introduce a new probabilistic model of the primes consisting of integers that survive the sieving process when a random residue class is selected for every prime modulus below a specific bound. From a rigorous analysis of this model, we obtain heuristic upper and lower bounds for the size of the largest prime gap in the interval $[1,x]$ [ 1 , x ] . Our results are stated in terms of the extremal bounds in the interval sieve problem. The same methods also allow us to rigorously relate the validity of the Hardy-Littlewood conjectures for an arbitrary set (such as the actual primes) to lower bounds for the largest gaps within that set.  more » « less
Award ID(s):
1802139 2301264
NSF-PAR ID:
10440641
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Inventiones mathematicae
Volume:
233
Issue:
3
ISSN:
0020-9910
Page Range / eLocation ID:
1471 to 1518
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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