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Friday, April 9, 2010

Prime numbers

I find the following identity rather intriguing...
$\sum_{k=1}^\infty\frac{1}{k} = \prod_{p \in P}\frac{1}{1-\frac{1}{p}}$.

The LHS of the equation is a sum over all positive integers $1,2,3 \dots$, the RHS of the equation is a product over all the prime numbers.

The prime numbers is the set of all integers which are (only) divisible by 1 and itself. There is no closed formula which generates the primes 2,3,5,7,11,13,17,19,23,29, ... There are approximately x / log x primes less than x.

Welcome to The Bridge

Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
To uncover hidden structures
To create new theorems and proofs
To boldly go where no man has gone before

(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)