TITLE:
On the Sum of Reciprocals of Mersenne Primes
AUTHORS:
Yoshihiro Tanaka
KEYWORDS:
Mersenne Primes, the Sum of Reciprocals, Unresolved Problem
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.7 No.2,
June
8,
2017
ABSTRACT: The sum of reciprocals of Mersenne primes converges
to 0.51645417894078856533···, which is an example of a probably infinite
subset of primes whose sum of reciprocals is finite and can be computed
accurately. This
value is larger than , where is the set of
perfect powers of prime numbers.