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Are infinitely many most primes in an a prime arithmetic progression of length at least 3?

Following the following two previous questions on mathoverflow:

http://mathoverflow.net/questions/34197/are-all-primes-in-a-pap-3/34298#34298

and

http://mathoverflow.net/questions/2214/covering-the-primes-by-3-term-aps

I have attempted to show that infinitely many primes are in an arithmetic progression of length 3 in the primes following Ben Green's comment that one can do this using the circle method; but I have not found any success. Can anyone suggest (with more detail perhaps) a way to show that infinitely many primes are in an arithmetic progression of length at least 3?

Edit: In view of the comments, I have rephrased the question: My intention was to ask what can one do (Ben Green suggested the circle method, but gave no details) to show that 'most' primes (that is, the exceptional set has upper density 0) are in an arithmetic progression of at least 3 in the primes.
show/hide this revision's text 1

Are infinitely many primes in an arithmetic progression?

Following the following two previous questions on mathoverflow:

http://mathoverflow.net/questions/34197/are-all-primes-in-a-pap-3/34298#34298

and

http://mathoverflow.net/questions/2214/covering-the-primes-by-3-term-aps

I have attempted to show that infinitely many primes are in an arithmetic progression of length 3 following Ben Green's comment that one can do this using the circle method; but I have not found any success. Can anyone suggest (with more detail perhaps) a way to show that infinitely many primes are in an arithmetic progression of length at least 3?