Terence Tao

He called it FactRat as a play on FortRat.

And he showed that you can program... It was too incomplete.

You could...

You could make a program that if your number you insert in was encoded as a prime, it would sink to zero.

It would go down, otherwise it would go up, and things like that.

So the general class of problems is really as complicated as all the mathematics.

Yeah, if you want to do it, not statistically, but you really want 100% of all inputs for the Earth.

Yeah, so what might be feasible is statistically 99%, you know, go to one.

But like everything, you know, that looks hard.

Riemann is up there.

P equals NP is a good one because that's a meta problem.

If you solve that in the positive sense that you can find a P equals NP algorithm, then potentially this solves a lot of other problems as well.

If the Riemann hypothesis is disproven, that would be a big mental shock to the number theorists.

But it would have follow-on effects for cryptography.

Because a lot of cryptography uses number theory, uses number theory constructions involving primes and so forth.

And it relies very much on the intuition that number theories have built over many, many years of what operations involving primes behave randomly and what ones don't.

And in particular, encryption methods are designed to turn

text with information on it into text which is indistinguishable from random noise.

And hence, we believe to be almost impossible to crack, at least mathematically.

But if something as core to our beliefs as the Riemann hypothesis is wrong, it means that there are actual patterns at the primes that we are not aware of.