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Large gaps between primes in subsets

By James Maynard

Appears in collections : Prime numbers and automatic sequences: determinism and randomness / Nombres premiers et suites automatiques : aléa et déterminisme, Fields medallists - 2022, The Fields Medallists

All previous methods of showing the existence of large gaps between primes have relied on the fact that smooth numbers are unusually sparse. This feature of the argument does not seem to generalise to showing large gaps between primes in subsets, such as values of a polynomial. We will talk about recent work which allows us to show large gaps between primes without relying on smooth number estimates. This then generalizes naturally to show long strings of consecutive composite values of a polynomial. This is joint work with Ford, Konyagin, Pomerance and Tao.

Information about the video

Date of recording 23/05/2017
Date of publication 01/06/2017
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19170903
Cite this video Maynard, James (23/05/2017). Large gaps between primes in subsets. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19170903
URL https://dx.doi.org/10.24350/CIRM.V.19170903

Domain(s)

Number Theory

Bibliography

Ford, K., Green, B., Konyagin, S., & Tao, S. (2015). Large gaps between consecutive prime numbers. <arXiv:1408.4505> - https://arxiv.org/abs/1408.4505
Maynard, J. (2016). Large gaps between primes. Annals of Mathematics. Second Series, 183(3), 915-933 - http://dx.doi.org/10.4007/annals.2016.183.3.3
Rankin, R.A. (1938). The difference between consecutive prime numbers. I. Journal of the London Mathematical Society, 13, 242-247 - http://dx.doi.org/10.1112/jlms/s1-13.4.242

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