Terence Tao

But what has been frustrating is that you combine the two together.

And suddenly you get an extremely rich, I mean, we know that there are statements in number theory that are actually as undecidable.

There are certain polynomials in some number of variables.

Is there a solution in the natural numbers?

And the answer depends on an undecidable statement, like whether the axioms of mathematics are consistent or not.

But even the simplest problems that combine something multiplicative, such as the primes, with something additive, such as shifting by two.

Separately, we understand both of them well, but if you ask, when you shift the prime by two, how often can you get another prime?

It's been amazingly hard to relate the two.

Right.

Yeah, so what we've realized because of this type of research is that different patterns have different

levels of indestructibility.

So what makes the twin prime problem hard is that if you take all the primes in the world, you know, 3, 5, 7, 11, so forth, there are some twins in there.

11 and 13 is a pair of twin primes, so forth.

But you could easily, if you wanted to, redact the primes to get rid of these twins.

The twins, they show up, and there are infinitely many of them, but they're actually reasonably sparse.

Initially, there's quite a few, but once you go to the millions, trillions, they become rarer and rarer.

And you could actually just... If someone was given access to the database of primes, you just edit out a few primes here and there, they could make the twin-prime conjecture false by just removing 0.01% of the primes or something.

Just well-chosen to do this.

And so you could present a...

censored database of the primes, which passes all of the statistical tests of the primes.