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Seminar

Analytic Number Theory Seminar: A construction of A. Schinzel: many numbers in a short interval without small prime factors. February 14, 2017 (02:00 PM PST - 03:00 PM PST)
Parent Program: Analytic Number Theory MSRI: Simons Auditorium
Speaker(s) Sergei Konyagin (V. A. Steklov Institute of Mathematics)
Description No Description
Video
We prove that, assuming the prime $k$-tuple conjecture, for large $x$ one can find $y$ so that the difference $\pi(x+y) - \pi(x) - \pi(y)$ is essentially larger than $x/(\log^2)x$.