While there are no other examples of consecutive primes, it's not difficult to find more pairs of consecutive integers with the same number of factors:
Eventually you get to sets of three consecutive integers with the same number of factors:
It isn't possible to have a sequence of more than three integers with only four factors, but so far I have found this set of four consecutive integers with six factors:
I'm sure that somewhere out there I can find out whether or not a) there are longer sequences of consecutive integers which the same number of factors and b) whether there is a natural limit to the process. That's as far as I can take it in the sleepless hours of the night though.