OFFSET
1,1
COMMENTS
Since prime(n) ~ n*log(n), Sum_{n>=1} prime(n)/n^j converges for j > 2.
EXAMPLE
3.339530...
The first few partial sums are:
up to prime(n)=2, 2/1^3 = 2.0;
up to prime(n)=3, 2 + 3/2^3 = 2.375;
up to prime(n)=5, 2 + 3/2^3 + 5/3^3 = 2.56018;
The partial sum for n <= 100000 is 3.3393903401...
The partial sum for n <= 1000000 is 3.33951457002...
The partial sum for n <= 5000000 is 3.3395274693...
The partial sum for n <= 10000000 is 3.339529222...
The partial sum for prime(n) <= 999999937 is 3.33953071535199...
CROSSREFS
KEYWORD
AUTHOR
Olivier Izad, Dec 30 2014
STATUS
approved