OFFSET
1,1
COMMENTS
Since prime(n) ~ n*log(n), Sum_{n >=1} prime(n)/n^j converges only when j > 2.
The partial sum over n <= 100000 is 2.33763532906803560, over n <= 1000000 is 2.337635329736982..., over n <= 5000000 is 2.3376353297446376... and over n <= 10000000 is 2.33763532974490000... - R. J. Mathar, Nov 05 2015
LINKS
Olivier Izad, Java program
EXAMPLE
2.3376353297449...
The first few iterations of the sum are:
n=1, 2/1^4 = 2;
n=2, 2 + 3/2^4 = 2.1875;
n=3, 2 + 3/2^4 + 5/3^4 = 2.249...
MATHEMATICA
s = 0; k = 1; p = 2; While[k < 100000001, s = N[s + p/k^4, 24]; k++; p = NextPrime@ p]; s (* Robert G. Wilson v, Jan 27 2015 *)
PROG
(bash)
awk 'BEGIN{n=1}; {sum=sum+$1/(n^4); n++; OFMT="%.50f"; print sum}' primes.txt
(Java) See attachment
(PARI) suminf(n=1, prime(n)/n^4) \\ Michel Marcus, Jan 10 2015
CROSSREFS
KEYWORD
AUTHOR
Olivier Izad, Dec 30 2014
STATUS
approved