What are the next several lines and how are they formed?

Do the sequences have any special feature?

Does the pattern continue indefinitely?

If I am right then the length of the terms 1, 2 ...200 ... is

{2,3,5,7,11,13,19,23,29,33,43,47,59,65,73,81,97,103,

121,129,141,151,173,181,201,213,231,243,271,279,309,325,

...,12233...}

and unbounded.

There is no way this sequence would be guessed  or found even with 200 terms.  So what is the point?