I am a "hobbyist mathematician", and I have an idea that relates Prime numbers, rational numbers, polytopes in n-dimensional lattices, and lattice point counting in those polytopes. For example, it can be used to calculate prime numbers by counting lattice points within (irrational) simplexes in n-dimensional space, where each dimension corresponds to a prime number. I've searched the web for similar ideas but haven't found any (perhaps I don't know the correct terminology). So, I'd like to throw this idea "out there" to see if it has any merit, and if it does have merit, whether it's already been done. My question is, what would be a good way to do this without wasting much of peoples' time and without suffering too much ridicule :-) if it turns out to be a terribly naive idea?
Note 12-04-16: edited to add Number-Theory and Soft-Question tags.
Well, I kept searching, and as AlgorithmsX suggested, I found this morning that the main element of my idea has already been described by others. This Wikipedia article describes key elements of the idea: https://en.wikipedia.org/wiki/Regular_number. In the Hasse diagram, the horizontal line for 7 is not accounted for by products of 2,3,5. My idea was to find a function to count lattice points within simplices formed by the origin (the number 1) and logarithms along the first n prime number dimensions, and as soon as the next integer could not be accounted for this way, it must be a prime (e.g., the number 7 in the diagram). Very much like the Sieve of Eratosthenes, Except I was looking for the lattice point counting function, rather than having to calculate every possible composite number leading up to n.
So, I consider my question closed for now. However, I'll keep playing with this subject, because it's fun. And any further comments / suggestions will be most welcome.