[SeqFan] sum of primes, product of primes

[Jud McCranie]

Sequence A2110 is the sum of the first n primes.  Let S(x) = the sum of the
primes < x.  Is the growth rate of S(x) known?  A quick check of the sum of
primes < 10^11 suggests that the growth rate is at least x^1.846, and of
course it is <= x^2.  Is there a more accurate growth rate known?

Sequence A7504 is the product of the first n primes.  If P(x) = log of
product of prime p = sum of log(p) for all p <= x, then empirically
log(P(x))/log(x) -> 1 as x -> infinity.  Is this correct?

+--------------------------------------------------------------------+
| Jud McCranie    jud.mccranie at mindspring.com  or   @camcat.com      |
|                                                                    |
| "We should regard the digital computer system as an instrument to  |
| assist the number theorist in investigating the properties of his  |
| universe - the natural numbers."  D. H. Lehmer, 1974 (paraphrased) |
+--------------------------------------------------------------------+