Prime number + 2 = Prime number

[Ivan Rancati]

EDIT: oops. Twin primes, plenty of study on that already. Sorry for the old news


I read this riddle in a 1950s encyclopedia (in Italian), and it piqued my interest.

Adding some prime numbers to 2 still yields a prime number
For example
3, 5
5, 7
11, 13
17, 19
41, 43
and so on

How could one possibly go about proving that there is an infinite number of these "prime pairs", or that past a certain prime number there is never going to be such a pair?


I would imagine there is already some conjecture about this, but not sure

cheers
Ivan