I have written an algorithm based on this assumption, of nonexistence of isolated groups of valid parans, but it fails some test cases.

Upon many trials I wrote a conformant solution and thus
I confirm the algorithm must be aware of many isoleted groups in order for the solution to be accepted.

in Haskell using a sieve of Erathostenes does not offer running time of below 12,000ms. I assume this is because the sieve is recomputed at each call to gap function.
Can you acknowledge that in your case you are using some static storage for the sieve ?