I think you may have meant “evenly divisible”. As far as proving an infinity, well good luck with that.
I would suggest that if you stipulate that there are an infinite amount of 'prime numbers' at your disposal, then there are an infinite amount of pairs.
NOW. The article started off describing primes separated by '2'. Then it goes on to discuss primes separated by larger (Much larger) amounts.
IS the original problem about primes separated by '2', or primes separated by any random number?
I don't see the problem being quickly unraveled if it's the latter.
Prove it for 2 x infinity, and divide result by 2.