Nonrecognizability of the unary prime language by REWB (conjecture)

Prove that regular expressions with backreferences without lookaheads (REWB) cannot recognize the unary prime language L_prime = { a^n : n is a prime number }, thereby separating REWB from REWBLk on unary languages.

Background

The paper demonstrates how REWBLk (which includes negative lookaheads) can recognize the unary prime language by constructing expressions that exclude non-primes, highlighting the utility of destructive and non-destructive lookaheads. This suggests a potential expressiveness gap between REWBLk and REWB (which lacks lookaheads).

The author explicitly conjectures that REWB cannot recognize the unary prime language, which, if established, would provide a concrete separation between REWB and REWBLk even over a unary alphabet.