Prescribing the binary digits of primes

Abstract

We present a new result on counting primes $p<N=2^n$ for which $r$ (arbitrarily placed) digits in the binary expansion of $p$ are specified. Compared with earlier work of Harman and Katai, the restriction on $r$ is relaxed to $r<c(\frac{n}{\log n}{)}^{4/7}$. This condition results from the estimates of Gallagher and Iwaniec on zero-free regions of $L$-functions with `powerful' conductor.

22 pages

Cited by in corpus (1)

• On Gaps Between Primitive Roots in the Hamming Metric