nt.number theory - Possible values for differences of primes

OK, I just saw this...a conjecture I made a few years ago covers this area

It relates d to OEIS A129912 entries, which are derived from the primorials.

Note that the d spoken to would only be a subset of those possible but these are guaranteed. A quick example is the prime 189239, which is offset from A129912(24) by 9059. So, the primes 189239 and 9059 have d=180180.

Note the "adjacency" part of the conjecture. The conjecture reads as follows:

"Every prime number >2 must have an absolute distance to a sequence entry (primorials, 

primorial products) that is itself prime, aside from the special cases prime=2 and those primes immediately adjacent to a sequence entry (primorials, primorial products).
The property is required but not sufficient ...it considers distances no larger than the candidate"

Rephrasing, this merely means every odd prime number must either be adjacent to, or a prime distance away from a primorial or primorial product. (the distance will be a prime smaller than the candidate)

Now obviously there are many other sets as you say ie 23-19,29-19,etc which lie outside the above.