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This is similar to

Enigma 295.This program recursively chooses a number to delete, but prunes away branches that can’t beat the current minimum. It runs in 41.6s.

Solution:The minimum score for N=30 is 103.One possible sequence is (13, 9, 15, 10, 8, 12, 14, 22).

Jim, I think that taking 13 is an illegal move because the Devil can’t respond. Instead 26 can removed any time after 10 and 2. That makes N = 116.

On the first move the Devil will always remove 1, so it’s your only opportunity to get rid of a prime. In fact, the only illegal first move would be to choose 1 itself.

Oh well! You’re right of course. Why didn’t I think of that?

Essentially the same approach.