FOM: fast-growing functions

[Thomas Forster]

I'm revising my lectures on BQOs and fast-growing
functions: Friedmannite combinatorics, that sort 
of thing.  I am in the market for examples of
fast-growing functions that the average 4th year
mathmo might find soothingly familiar, and i 
started wondering about prime pairs.  Does anybody
know whether there is a lower bound on the growth
rate of the function that enumerates the lower
members of prime pairs?  I take it it's still open
that there are infinitely many?
     
    Thomas Forster