Partial sum is 0.81571010760865175... if primes up to 40 binary digits are included; partial sum is 0.8157101534554485... if summed to 42 binary digits. - R. J. Mathar, Aug 27 2011
Partial sum is 0.81571019628323164... for primes up to 66 bits. - Martin Raab, Jan 13 2012