Starting at 10, for any set of 5 consecutive odd numbers, at most 4 can be prime (the number ending in 5 cannot be prime). Moreover any such set has to have the number ending in 5 as the middle of two pairs of prime (you cannot have 3 consecutive odd primes when you start after 10). The first example of such a set is 11, 13, 17, 19. The next is 101, 103, 107, 109. How frequently does such a sequence occur? Is it known if there are an infinite number of such pairs of pairs?