andrel <a_l### [at] hotmailcom> wrote:
> WTH has the fine structure constant that silly value of nearly 1/137?

  One would expect chaos and unexplained numbers in physics. It has for
long fascinated me that there is a lot of chaos and unexplained numbers
in pure mathematics too.

  Prime numbers are a prime (no pun intended) example. They are the
quintessential form of chaos and unpredictability in mathematics.

  If you think about prime numbers as a result of the sieve of Eratosthenes,
they are rather simple, really: Any multiple of a prime is not a prime.
If you think how you would construct a list of primes using this sieving
technique, it's quite simple and straightforward. One could hastily think
that primes are very regular and predictable this way. One would be very
wrong.

  Many of the unsolved problems in mathematics are relatively simple
problems related to primes. Problems which have been puzzling mathematicians
even for centuries. That's how unpredictable they are.

  The thing which fascinates me is: Why? Why is there such an unpredictable
chaos as a result of such a simple thing?

  Individual results sometimes fascinate me too. For example, the smaller
counter-example to the Polya conjecture is 906150257. Why precisely that
value? What's so special about that value that it breaks the conjecture?
Why there and not somewhere else?

-- 
                                                          - Warp

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