[SeqFan] sum of primes, product of primes
Jud McCranie
jud.mccranie at mindspring.com
Sun Jul 12 01:09:19 CEST 1998
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) |
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