Yes, apart from the

Yes, apart from the "sufficiently large" and allowing prime + prime as well as prime + semiprime. The parity problem makes the latter hard, but some progress has been made, see arXiv:math/0609615 and arXiv:0803.2636. (The key progress is their use of E2 = semiprimes rather than P2 = primes or semiprimes.)


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