Prime numbers with Beatty sequences

By William D. Banks, Igor E. Shparlinski. 2007

50 citations recorded by the source corpus.

A study of certain Hamiltonian systems has lead Y. Long to conjecture the existence of infinitely many primes of the form $p=2[\alpha n]+1$, where $1 0$ depends only on $\alpha$. We also prove a similar result for primes $p=[\alpha n+\beta]$ such that $p\equiv a\pmod q$.

Subfields: Algebra and Number Theory, Geometry and Topology, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/b280a7b8dd61ba635f1209dd711365ddb485b131