Demented

Big Day at Google: it's their 20th anniversary. Hooray!

Here's my little scribble for today, on a BIG question.

What is the Reimann hypothesis, and how does it involve
prime numbers. The best account of that I have found of
that - thank you, Google - is on the encyclopedia Britannica,
referenced below:

https://www.britannica.com/science/Riemann-zeta-function

Here is the second paragraph where I have highlighted in red an
assertion which might seem little odd. Why should x greater than
1 converge to a number when other values yield an infinite sum??:

"When x = 1, this series is called the harmonic series, which increases
without bound—i.e., its sum is infinite. For values of x larger than 1, 
the series converges to a finite number as successive terms are added. 
If x is less than 1, the sum is again infinite. The zeta function was known
to the Swiss mathematician Leonhard Euler in 1737, but it was first
studied extensively by the German mathematician Bernhard Riemann."

On reflection, what is going on is this case is not  true addition of value
but merely an unveiling of more precision; one ends up extending the number
of decimals. It is a case of what I think if as the Demented Dieter Dilemna.
My weight is at the perfect point , but I still want to add more rice to the soup
every night. This will only work if I add an ever smaller amount
that never goes over the critical point which maintains my weight.

In the context of number theory, the Riemann extension of the zeta function
to a statement with complex numbers, is trying for a digit-free formulation.
It is no surprise that it will need to call on prime numbers...