Large gaps between primes in subsets
Recent developments in Analytic Number Theory May 01, 2017 - May 05, 2017
Location: MSRI: Simons Auditorium
primes in polynomials
density of primes
small gaps between primes
consecutive composites in polynomials
11N32 - Primes represented by polynomials; other multiplicative structure of polynomial values
11N64 - Other results on the distribution of values or the characterization of arithmetic functions
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
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