Gerasimovian Primes of the form 2310n + 1, primorial analogues, and so forth

[Jonathan Post]

Are we to expect Juri-Stepan Gerasimov to soon submit (I say pre-emptively):

Primes of the form 2310n + 1
2311, 4621, 9241, 11551, 18481, 25411, 32341, 34651, 43891, 50821, ...

Primes of the form 2310n + 13
13873, 16183, 18493, 25423, 27733, 32353, 36973, 41593, 48523, 50833, ...

etcetera

Primes of the form 30030n + 1
120121, 150151, 180181, 270271, 300301, 330331, 390391, 420421,
450451, 540541, ...

Primes of the form 30030n + 17
30047, 60077, 90107, 240257, 270287, 300317, 330347, 390407, 540557, 570587, ...

etcetera

Primes of the form 510510n + 1
4084081, 5105101, 8168161, 8678671, 9189181, 10720711,  12762751,
13273261, 13783771, 14804791, ...

etcetera

and, if so, what does this classification buy for us, in terms of
understanding, or internal OEIS coherence?

Just asking...