@lcamtuflcamtuf
Is that ("pick a large even number, subtract one prime from it, and get another for free") true often enough to be useful?
I checked for a couple of small numbers and e.g., there are 550 primes under 4000, but only 130 of them yield a second prime when subtracted from 4000. (24%) At 40000 it's only 18% of the time.