Highly Influenced

# PRIME NUMBERS WITH BEATTY SEQUENCES

@inproceedings{IUM2009PRIMENW, title={PRIME NUMBERS WITH BEATTY SEQUENCES}, author={COLLOQU IUM and MATHEMAT ICUM and Igor E. Shparlinski}, year={2009} }

- Published 2009

A study of certain Hamiltonian systems has led Y. Long to conjecture the existence of infinitely many primes which are not of the form p = 2bαnc + 1, where 1 < α < 2 is a fixed irrational number. An argument of P. Ribenboim coupled with classical results about the distribution of fractional parts of irrational multiples of primes in an arithmetic progression immediately implies that this conjecture holds in a much more precise asymptotic form. Motivated by this observation, we give an… CONTINUE READING