I've been doing some meddling in places I should'nt be, namely the world of advanced mathemaitcs. And I've jusy been struck by something that leaves me wondering...
This could just be my ignorance talking/writing, but I figure the best way to cure ignorance is to broadcast it for the world to see, some doctor should come along and give a cure in the form of knowlrdged and a vaccine in the form of humility and inqusitiveness.

Disgressions aside, I was reading when I stumbled upon the Twin Prime conjecture, which is still listed as an unsolved problem.
Them my mind strayed to the Green-Tao Theorem, which states that for any natural number k, there exist k-term arithmetic progression of primes.

Possibly due to my ignorance, I make a leap of intuition and assue that if you set k=2, then you discover your twin primes.
Looking it up on the internet, I see that the Green-Tao theorem implies that the Twin Prime conjecture is true. Why?
I'm seeing a possible Fields Medal here, (or at least a Wolf or an Abel Prize).
So could someone please burst my bubble and explain this situation to me?
If not , I see a few prizes in my future.

Edit:
A thought just struck on my cerebellum, is it because while the Green-Tao theorem states that there exists sequences of primes with a difference of 2, it doesen't state the number of such primes, or whether such primes are finite or infinite?

If you let k=2 then the theorem says that there is a sequence of two terms that are in arithmetic progression. That is absolutely trivial. Saying k=2 does not mean they have to be prime-twins. There is a difference between prime-twins and arithmetic progressions of primes.

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