Harristotelian Logic

I think that "but why?" is the question of the true scientist and that's where things get interesting.

But why?

So you can ask, why would primes care what residue they have modulo some other prime?

If they do not, then residues of one prime modulo another behave randomly.

If so, then EVERY random sequence of two elements only can be represented as being somewhere on the line of p mod 3.

So if you flip a coin for a while you can get some computer to do a search and if it's not too far out, you'll find that sequence of flips in the sequence of p mod 3.

Or, there is an underlying pattern where some prime like 37 PREFERS to have a residue of 1 modulo 3, and if you can figure out that underlying pattern you can get some sense of some special rules that govern primes, but, composites are products of primes! So they'd reflect that pattern, right?

I am not the first person to suggest randomness in this area.

I suspect mathematicians have demonized the others who have.

Why?

Because if p mod 3 is random, as in, there is no rhyme nor reason to why any particular prime has 1 or 2 as its residue modulo 3 than it just does, then huge areas of funding in the math field collapse.

Quite simply, math people no longer get paid in those areas, and mathematicians who specialize in those areas would have to find somewhere else to do research!

But what if p mod 3 IS random? Then you would know that ANY random behavior in our real world would have to be represented within the infinite sequence of primes modulo some other prime, and that bit of "pure math" would have real world application in physics!