Thanks to James Davis — who stands to collect $1000 for finding a counterexample to a John H. Conway conjecture (see the video here, from 19:20 to 22:30):
13532385396179 = 13 * 53^2 * 3853 * 96179
Very nice! I'm glad it ended up this way. When I wrote my Climb to a prime piece on 12 October 2014, I was under the distinct impression that it would have been enough to evolve the number 20 to a prime in order to claim the prize. I now see that Bill Cheswick's "Five $1000 Problems" pdf was last updated 13 October 2014 — one day later — and I no longer read it that way.