Considering the prime number distribution is disjointed by a sequence of steps it is possible to explain, in part, some of the longest gaps in the prime number distribution:
The first gap of 4 (between 7 and 11) is between the patterns starting at 4 and 9
The first gap of 6 (between 23 and 29) is between the pattern starting at 9 and 25
The first gap of 14 (between 113 and 127) is between the pattern starting at 49 and 121.
However there are other large gaps which are not explained in this way (some of which appear to be equally explainable).
Smaller gaps are often (but not always) repeated throughout the distribution of prime numbers at a length of p# (as a result of primes being in helices). These are often not obvious as they are included within larger gaps; however it is possible to give a good indication of where primes will NOT be and where pairs of primes will NOT be.