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
On Tue, 13 Jul 1999, Lucas Wiman wrote:
So for numbers 2^n (in Base 10), [or is it 2^p?] there are a lot more leading
ones than one would "expect" naievely (you would expect 1/9 to start with
"1", I imagine).
Yes. Though they were talking about the exponents...
Here are the percentages
At 12:38 AM 7/13/99 -0400, Lucas Wiman wrote:
Here are the percentages for the first 3000 powers of 2. The first collumn
is the percentage, the second is the difference from the predicted Benford
percentage. Weird, I would have thought that it wouldn't affect powers of
two...
That's the type
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
I've noticed that with any odd number you can make the formula x^2 -
y^2 = n where n = the odd number and x - y and x + y are factors of n.
I was just wondering if one could use the graph of a hyperbola to see
only the possible integer values of x and y.
At 09:05 AM 7/13/99 -0400, Chip Lynch wrote:
In some vague attempt to not take the Benford issue off topic, it's
interesting that numbers 2^n (for all Natural numbers n) follows the
pattern VERY closely,
In the limit as n - infinity, 2^n must follow the law exactly. Almost by
definition.
Brian Beesley wrote:
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
Steven Whitaker wrote:
Maybe it's my imagination, but it seems to me that the factors of the
prime exponent Mersenne numbers start with a 1 more often than a 2 or
3 etc. Are they obeying Benford's law too?
For instance, for the 10 primes from 5003 to 5081, there are 20 known
factors. 10 of
