If Omega maintains a 99.9% accuracy rate against a strategy that changes its decision based on the lottery numbers, it means that Omega can predict the lottery numbers. Therefore, if the lottery number is composite, Omega has multiple choices against an agent that one-boxes when the numbers are different and two-boxes when the numbers are the same: it can pick the same composite number as the lottery, in which case the agent will two-box and earn 2,001,000, or it can pick a different prime number, and have the agent one-box and earn 3,001,000. It seems like the agent that one-boxes all the time does better by eliminating the cases where Omega selects the same number as the lottery, so I would one box.