Re^2: Mean of 10^9 consecutive primes?

[Richard Mathar]

zs> From zakseidov at yahoo.com  Thu Sep 28 11:45:15 2006
zs> Date: Thu, 28 Sep 2006 02:45:11 -0700 (PDT)
zs> Subject: Re: Mean of 10^9 consecutive primes?
zs> To: Richard Mathar <mathar at strw.leidenuniv.nl>, seqfan at ext.jussieu.fr
zs> 
zs> Right now I'm trying to calculate 
zs> sum of first 10^9 primes... using Mathematica... spent
zs> already hours...
zs> ...
zs> Just for control:
zs> 
zs> n=106333207,s=112600741085770645
zs> 
zs> (n may be correct up to =/- 1 because
zs> interrupting Mathematica may cause it(?))

The sum of primes starting at p=2 =prime(1), accumulating 106333207 terms
as if to compute A007504(106333207),
we get the following PARI sequence of partial sums:

#primes     sum=A007504
1           2
2           5
3           10
..
758366 4212213162643
758367 4212224680542
..
1502066 17353951972775
..
2880000 66692605951677
..
7310000 456255316540099
..
19880000 3584883605837159
..
25260000 5868859333341447
25270000 5873641089786693
25280000 5878424839658977
..
41910000 16627062191706423
41920000 16635219816776011
..
90800000 81418246408178901
90810000 81436660732646801
..
100830000 100961837110105179
100840000 100982396851892505
..
102260000 103923670141862609
102270000 103944536764897023
..
105670000 111163631669338771
105680000 111185230615130909
..
106333204 112600736737687553
106333205 112600738911729084
106333206 112600741085770645
106333207 112600743259812234

This is based on PARI's nextprime(), which might smuggle
some pseudo-primes in, the probability of which I cannot estimate
right now. So far the results are compatible.

Richard, http://www.strw.leidenuniv.nl/~mathar