24961[PrimeNumbers] Re: Caldwell conjectured #Wieferich primes = finite?
- Mar 26, 2013David wrote:
> I incline to the Crandall-Pomerance heuristicMe too. I have also been planning to ask Chris. In fact I have a whole file
> that there is an infinitude, with O(log(log(N)))
> less than N. (CP Section 1.3.3.)
with comments to the Prime Pages. I should probably get around to actually
mailing it to him one day before it all becomes obsolete. Below is what it has
said for a long time.
"Are there infinitely many Wieferich primes? Probably not"
I wonder what "Probably not" is based on. The Crandall, Dilcher and Pomerance
reference says on page 14 of
"Thus, heuristically we might argue that the number of Wieferich primes in an
interval [x; y] is expected to be sum(1/p) over x<=p<=y ~= ln(ln y/ln x)."
This is the same as the estimate on
(The reason for the estimates is the same: A guess that each p has chance 1/p)
Jens Kruse Andersen
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