Terence Tao

It obeys things like the prime number theorem and other things about the primes, but doesn't contain any twin primes anymore.

And this is a real obstacle to the twin prime conjecture.

It means that any

proof strategy to actually find trend primes in the actual primes must fail when applied to these slightly edited primes.

And so it must be some very subtle, delicate feature of the primes that you can't just get from like aggregate statistical analysis.

Okay, so that's out.

Yeah.

On the other hand, arithmetic progressions has turned out to be much more robust.

You can take the primes, and you can eliminate 99% of the primes, actually.

And you can take any 99% you want.

And it turns out, and another thing we proved, is that you still get arithmetic progressions.

Arithmetic progressions are much, you know, they're like cockroaches.

Of arbitrary length.

Yes.

Yes.

That's crazy.

Yeah.

Yeah.

But it's again like, it's an infinite monkey type phenomenon.

For any fixed length of your set, you don't get arbitrary length progressions.