As of May 4 2007 the scripts will autodetect your timezone settings. Nothing here has to be changed, but there are a few things

## Thursday, September 8, 2011

### Prime?

A prime p is a number with two positive divisors: 1 and p. Note how this definition nicely excludes 1 which has only one positive divisor. Then the primes are: $$2,3,5,7,11,13,17,19,23,29, \cdots$$
$$5 = -i \cdot (1 + 2i) \cdot (2 + i)$$
This is an example of a factorization in the quadratic field of Gaussian Integers. It is therefore not enough to say that a number is prime. Primality is relative in relation to the number field.

The mathematician Lamé thought to have cracked Fermat's Last Theorem in 1847. Needless to say that his proof contained an error. He overlooked the fact that prime factorization was not unique in a number system he used in his proof.

In Mathematica factorization is done with:

FactorInteger[n],

factorization using Gaussian integers is done with:

FactorInteger[5, GaussianIntegers -> True].

## 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.)