This first becomes apparent with the bases 5 and 7; all subsequent primes can be stated as multiples of 3#, adding a base of either 5 or 7.
The next alignment occurs using the eight bases 11, 13, 17, 19, 23, 29, 31, 37. All subsequent primes can be stated as multiples of 5#, adding one of these 8 bases.
Subsequent alignments are based on larger numbers of bases as each p# is considered. At the next the number of bases becomes 48 and the interval 7# or 210.
The question arises are primes balanced between bases? Are there as many primes based on 5 as 7? Over short lengths of primes this is not the case; but over longer runs there seems to be some balance.
Similarly, the 8 bases listed above, there seems to be some sort of balance, but it is anticipated there will be fluctuations but possibly no long term bias?
A nice project for some student?