[fieutgtv] sum of the reciprocals of known primes

at the time of writing, the largest known prime number is the Mersenne prime 2^136279841 - 1, a 41-million-digit number.

the sum of the reciprocals of all primes up to the largest known prime can be estimated to be approximately

log(log(2^136279841 - 1)) + 0.261497 ~= 18.6252

, where the offset 0.261497 is the Meissel-Mertens constant (known to many more digits).  (how many more?)

(previously, on log(2^n +1).)

however, the sum of the reciprocals of all primes up to infinity is infinity, i.e., the infinite sum diverges (proven by Euler).  despite our finite sum being up to a huge prime, 18.6 is still a long way from infinity.

the reciprocal of the next prime after the largest known prime ("the first unknown prime") will add approximately 10^-41000000 to our partial sum 18.6252 , a tiny step.  and each additional step will be yet smaller, because reciprocals keep getting smaller.  yet infinity will still eventually be "reached": the sum will exceed any finite number you can think of: Graham's number, Rayo's number, Loader's number, etc., (and all finite numbers you can't think of).

previously, computing the sum one button press at a time.