If you're having math problems, I feel bad for you, son...

[tama]

33. You're on an interesting track

Consider also the fundamental theorem of arithmetics: "any integer greater than 1 can be written as a unique product (up to ordering of the factors) of prime numbers." http://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic

Matti Pitkänen has developed the notion of infinite primes:
http://tgd.wippiespace.com/public_html/pdfpool/infpc.pdf

Second chapter of the paper begins with:

2 Infinite primes, integers, and rationals

The definition of the infinite integers and rationals is a straightforward procedure and structurally similar to a repeated second quantization of a super-symmetric quantum field theory but including also the number theoretic counterparts of bound states.

2.1 The first level of hierarchy

In the following the concept of infinite prime is developed gradually by stepwise procedure rather than giving directly the basic definitions. The hope is that the development of the concept in the same manner as it actually occurred would make it easier to understand it.

Step 1
One could try to define infinite primes P by starting from the basic idea in the proof of Euclid for the existence of infinite number of primes. Take the product of all finite primes and add 1 to get a new prime:
P =1+X ,