Re: Prime numbers

In article <1152560414.268943.54580@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
luiroto@xxxxxxxxx wrote:

luiroto@xxxxxxxxx wrote:
Prime numbers are an example of arithmetical Chaos., as the
Collatz sequence, as the digits of an irrational number, or the
product of the iteration of y = 2*y^2 -1 with 0 < y(0) < 1.

.101001000100001000001000000100000001000000001... is
an irrational number. Its digits don't look very chaotic to me.
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)

Your remark is true.
I should have said : As some irrational numbers as the square root
of a number not perfect square , some trascendental constants
as pi, e, sin(1) and log(2) or the results of the iteration of:
y(n+1) = 2 * y(n) ^ 2 - 1 beguining with the seed 0<y(0) <1
and y(0) <> .5
Ludovicus

If you can prove that the digits of the square root of 2
(or of pi, or e, or sin 1, or log 2 - take your pick)
are "an example of arithmetical chaos," if you can prove
anything whatever about the digits of these numbers (beyond
their aperiodicity), then you've earned undying fame.
Start by proving that there are infinitely many sevens
in the decimal for the square root of 2.

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)
.

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