On 12 Jul 99, at 17:45, Lucas Wiman wrote:
> That's the point of Benford's law, it is supposed to be relatively independent
> of the set of numbers.
... within reason ?
If I take the (decimal) powers of 0.999 and get bored after 100
trials, I find they _all_ start with a 9 ;-)
> Note that in the set of mersenne prime exponents (so far), the leading
> digit 1 (in decimal), turns up 10 times as opposed to the 4.2 times
> expected by equal leading digit distribution...
Actually we should expect an excess of smaller leading digits over
that predicted by "Benford's Law" in this case. A smaller exponent is
more likely to be prime than a larger exponent, and a smaller prime
exponent is more likely to give rise a Mersenne prime than a larger
prime exponent. "Benford's Law" would follow if _every_ exponent
(prime or composite) was equally likely to give rise to a Mersenne
prime.
[Different message, same author]
> Yes. Though they were talking about the exponents...
> Weird, I would have thought that it wouldn't affect powers of
> two...
Why not? Looks like a perfect model to me!
Regards
Brian Beesley
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