I have a particle system with X particles. Each particle tests for collision with other particles. This gives X*X = X^2 collision tests per frame. For 60f/s, this corresponds to 60*X^2 collision detection per second.

What is the best technological approach for these intensive calculations? Should I use F#, C, C++ or C#, or something else?

The following are constraints

1. The code is written in C# with the latest XNA
2. Multi-threaded may be considered
3. No special algorithm that tests the collision with the nearest neighbors or that reduces the problem

The last constraint may be strange, so let me explain. Regardless constraint 3, given a problem with enormous computational requirement what would be the best approach to solve the problem. An algorithm reduces the problem; still the same algorithm may behave different depending on technology. Consider pros and cons of CLR vs native C.