Indeed all known $n$ for which $d_nd_n \geq p_n$ occurs are $n=30,11,9,6,4$ and $2$, so there are very few opportunities for something like $ab \geq p_{n+1}$ to happen.

It is believed that there are only finitely many gaps g (with adjacent prime p) such that g^2 > p, and the largest of these has p=113. My vote is that L is the same as Q, based on Anthony's analysis and Robert's results.

If I were a referee, I would appreciate having an addendum consisting of a note saying in effect, "I prefer to reference this step, rather than include it", and the five pages justifying the step, so that I the referee don't have to hunt it down. Maybe the referee will help improve on the five pages, or agree with you that the step does not need justifying. If you do a lot to accommodate the referee, the referee might return the favor.

If the b_i are a permutation of the a_i, all positive x satisfy the equation. You might consider the case m=n=2 first before looking at longer tuples.

Also, many of the examples can be sieved out with small primes, for example all those candidates for p that are 2 mod 7.

Even from an algebraic standpoint, this is of interest. If it were pure subset, this would speak of transitivity. Equality and superset imply a form of divisibility. I'm still considering the algebraic aspects. Are you also interested in such relations on topological groups? It's conceivable that there is literature on this notion for topological algebras.

@ZsbánAmbrus , yes, all of the regions discussed are the same shape and orientation. If rotation or reflection were allowed, I could loosely pack two very obtuse triangles in a larger triangle.

Are you assuming convex C, or is this even more general? In any case it is looking like a good argument.

It should be the case that the enclosing region C has the same orientation as the packed regions. There are pentagons P where a packing exists if the outer pentagon is rotated with respect to the inner pentagons.

When k=b I get k! for the complement. It might start a nice recurrence for the complement.

Too bad. I found it at a public library in the U.S. Maybe interlibrary loan?