sum of first 10^n primes A099824

[cino hilliard]

Hi, fans, Zak

I  extended the sum of the first 10^n primes to a(11) which took 30 hours. 
Below is a copy and
paste.  I will try to do a(12) which will take about 12 days later. More 
comments are below.
Included below is a pari program that will do this in about 21 days.

The sieve files which are good for ranges up to 2^64 are at

http://tech135436174616790299414111.groups.yahoo.com/group/seqfun/files/

Because we can compute the sums of primes in ranges, group efforts with 
several computers
could be used to attain sums of the first pi(10^15) primes.

Subject: COMMENT FROM cino hilliard RE A099824

%I A099824
%S A099824 2, 129, 24133, 3682913, 496165411, 62260698721, 7472966967499, 
870530414842019,
99262851056183695, 11138479445180240497, 1234379338586942892505,
135436174616790299414111
%C A099824 Extended sequence with a(11) using the program at the link. Here 
is the output.
f:\eratosieve>sumprimes 2760727302517
Sqrt stop =  1661543
Extending sieve size to 2097152
Memory Used 6881312
# {(null) <= Primes <= 2760727302517} = 100000000000
Sum estimate = stop^2/(2*log(stop)-1) - start^2/(2*log(start)-1)
Sum of primes  = 135436174616790299414111
Sum Estimate   = 135391808968751853087450
Relative Error = 0.00032757605686939417
Sec = 107301.765625 = 30 hrs with multitasking.

For speed purposes we maintain the logic of summing primes less than a 
number.
Since 2760727302517 is the (10^11)th prime, summing the primes less than or
equal to 2760727302517 will give us the sum of the first 10^11 primes. The
relative error indicates there is a high probability the value is correct.
The simple Pari program below will compute the sum of the first 10^11 primes
in about 21 days. Someone may want to verify this with Pari.

Using the sieve program which is good up to 2^64, we can compute a(10^12) in
about 12 days. I was going to do this and submit both but power 
interruptions
talked me out of it. When I purchase an uninterruptable power supply, I will
background the sieve program for a(10^12).
%H A099824 C. Hilliard, <a 
href="http://tech.groups.yahoo.com/group/seqfun/files/">Sumprimes</a>.
%o A099824 (PARI) sumprimes(n) = a=1;sum(x=1,n,a=nextprime(a+1))
%O A099824 1
%K A099824 ,nonn,
%A A099824 cino hilliard (hillcino368 at hotmail.com), Oct 03 2006

Somehow the comments are still not not passing to my email  normally.

Enjoy,
Cino