Summing the Reciprocals of Primes

The sum of the reciprocals of the primes diverges, but very slowly. The sum of the reciprocals of the first 100 primes is 2.106 The sum of the reciprocals of the first 1,000 primes is 2.457 For the first 10,000 it s 2.709 And it keeps creeping up, ever more slowly. To get the sum to [ ]