I initially thought two-box, but on thinking about it more, I'm going for one-box.

For simple numbers, let's suppose that the lottery has a 50% chance of choosing a prime number, and that if Omega could select the same number as the lottery, he'll do so with 10% probability.

Three simple strategies:

1) Always one-box: Gets Omega's payout every time, wins the lottery 50% of the time. Average total payout $2M. (numbers are the same 10% of the time when the lottery is 'prime')

2) Always two-box: Omega never pays out, wins the lottery 50% of the time. Average total payout $1.001M. (numbers are the same 10% of the time when the lottery is 'composite')

3) Normally one-box, two-box when numbers are the same. Omega pays out 95% of the time. Lottery pays out 50% of the time. Average total payout $1.95M. (Numbers are the same 10% of the time when the lottery is 'composite')

The trick is that the question tries to lead you to the wrong counterfactual by drawing your attention to the situation where the numbers are the same. Whether you see the numbers being the same depends on your decision. In the counterfactual world where you decide something else, the lottery number doesn't change to match Omega's prediction. Instead, in the counterfactual world, the lottery number and Omega's number are different.