This seems like the "obvious" answer, at least in the timeless sense.
Maybe, but obvious answers to such problems are often wrong. Often, multiple different answers are each obviously the exclusively right answer. And look at all the people in this thread one-boxing. Not so obvious to them.
My reasoning was as stated, but I'm not going to use its "obviousness" as an additional argument in favour of it. And on reading the comments and the Facebook thread, I notice that I have neglected to consider the hypothetical situations in which the two numbers are different. On considering it, it seems that I should still argue as I did, using all the available information, i.e. that on this occasion the two numbers are the same. But it is merely obvious to me that this is so; I am not at all certain.
the obvious solution is unlikely to be fully correct, or else what would be the point of Eliezer posing the problem in the first place...
I'm disinclined to guess the right answer on the basis of predicting the hidden purposes of someone smarter than me. But I can, as it happens, think of a reason for posing a question whose "obvious" solution is completely right. It could be just the first of a garden path series of puzzles for which the "obvious" solutions are collectively inconsistent with any known decision theory.
But it is merely obvious to me that this is so; I am not at all certain.
Upvoted for awesome epigram.
You see two boxes and you can either take both boxes, or take only box B. Box A is transparent and contains $1000. Box B contains a visible number, say 1033. The Bank of Omega, which operates by very clear and transparent mechanisms, will pay you $1M if this number is prime, and $0 if it is composite. Omega is known to select prime numbers for Box B whenever Omega predicts that you will take only Box B; and conversely select composite numbers if Omega predicts that you will take both boxes. Omega has previously predicted correctly in 99.9% of cases.
Separately, the Numerical Lottery has randomly selected 1033 and is displaying this number on a screen nearby. The Lottery Bank, likewise operating by a clear known mechanism, will pay you $2 million if it has selected a composite number, and otherwise pay you $0. (This event will take place regardless of whether you take only B or both boxes, and both the Bank of Omega and the Lottery Bank will carry out their payment processes - you don't have to choose one game or the other.)
You previously played the game with Omega and the Numerical Lottery a few thousand times before you ran across this case where Omega's number and the Lottery number were the same, so this event is not suspicious.
Omega also knew the Lottery number before you saw it, and while making its prediction, and Omega likewise predicts correctly in 99.9% of the cases where the Lottery number happens to match Omega's number. (Omega's number is chosen independently of the lottery number, however.)
You have two minutes to make a decision, you don't have a calculator, and if you try to factor the number you will be run over by the trolley from the Ultimate Trolley Problem.
Do you take only box B, or both boxes?