## Tuesday, June 8, 2010

### Question for Aliens.

Dear people
Perhaps someone is in contact with Cosmic Visitors or Aliens or ETs. OR knows some CONTACTEE.
If so, PLEASE, ask our alien brothers to tell us the solution of the Riemann Hypothesis about Prime Numbers.
It's a mathematical problem that remains unsolved. Thanks.

http://en.wikipedia.org/wiki/Prime_number#The_Riemann_hypothesis

The Riemann hypothesis
Main article: Riemann hypothesis

To state the Riemann hypothesis, one of the oldest, yet, as of 2010, unproven mathematical conjectures, it is necessary to understand the Riemann zeta function (s is a complex number with real part bigger than 1)

\zeta(s)=\sum_{n=1}^\infin \frac{1}{n^s} = \prod_{p \text{ prime}} \frac{1}{1-p^{-s}}.

The second equality is a consequence of the fundamental theorem of arithmetics, and shows that the zeta function is deeply connected with prime numbers. For example, the fact (see above) that there are infinitely many primes can be read off from the divergence of the harmonic series:

\zeta(1) = \sum_{n=1}^\infin \frac{1}{n} = \prod_{p} \frac{1}{1-p^{-1}} .

If there were a finite number of primes then ζ(1) would have a finite value - but instead we know that the Riemann zeta function has a simple pole at 1.

Another example of the richness of the zeta function and a glimpse of modern algebraic number theory is the following identity (Basel problem), due to Euler,

\zeta(2) = \prod_{p} \frac{1}{1-p^{-2}}= \frac{\pi^2}{6}.

Riemann's hypothesis is concerned with the zeroes of the ζ-function (i.e., s such that ζ(s) = 0). The connection to prime numbers is that it essentially says that the primes are as regularly distributed as possible. From a physical viewpoint, it roughly states that the irregularity in the distribution of primes only comes from random noise. From a mathematical viewpoint, it roughly states that the asymptotic distribution of primes (about 1/ log x of numbers less than x are primes, the prime number theorem) also holds for much shorter intervals of length about the square root of x (for intervals near x). This hypothesis is generally believed to be correct. In particular, the simplest assumption is that primes should have no significant irregularities without good reason.
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