Variable Prime "Twins"
Brachylog, 27 23 bytes

:1f
hS,?tye.:S+:.L*$pL,


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Predicate 0 (main predicate)

:1f                     Find all solutions of predicate 1
                        given Input as Input,
                        Unify Output with the set of all solutions.


Predicate 1 (auxiliary predicate)

hS,?tye.:S+:.L*$pL,

hS                      the first element of Input is S,
   ?tye.                Output is an element between 0 and
                        the last element of Input,
       .:S+:.L          The list [Output+S,Output] is L,
             L*$pL      The product of L, prime-factorized, is still L