Tight upper and lower bounds for the reciprocal sum of Proth primes

  title={Tight upper and lower bounds for the reciprocal sum of Proth primes},
  author={Bertalan Borsos and Attila Kov{\'a}cs and Norbert Tihanyi},
  journal={The Ramanujan Journal},
Computing the reciprocal sum of sparse integer sequences with tight upper and lower bounds is far from trivial. In the case of Carmichael numbers or twin primes even the first decimal digit is unknown. For accurate bounds the exact structure of the sequences needs to be unfolded. In this paper we present explicit bounds for the sum of reciprocals of Proth primes with nine decimal digit precision. We show closed formulae for calculating the nth Proth number $$F_n$$ F n , the number of… 



Primes with a Prime Subscript

It is shown, with the aid of a computer, that every integer greater than 96 is representable as a sum of distinct members of the sequence {q~}.

Improved Bounds on Brun’s Constant

This work improves the unconditional bounds on Brun's constant to 1.840503 < B < 2.288513, which is about a 13\% improvement on the previous best published result.

Problems concerning prime numbers (Hilbert’s problem 8)

  • Proceedings of Symposia in Pure Mathematics
  • 1976