If the agent is EDT and Omicron chooses a prime number, then Omega has to choose a different prime number. Fortunately, for every prime number there exists a distinct prime number.
EDT’s policy is not “two-box if both numbers are prime or both numbers are composite”, it’s “two-box if both numbers are equal”. EDT can’t (by hypothesis) figure out in the allotted time whether the number in the box (or the number that Omicron chose) is prime. (It can readily verify the equality of the two numbers, though, and this equality is what causes it—erroneously, in my view—to believe it has control over whether it gets paid by Omicron.)
If the agent is EDT and Omicron chooses a prime number, then Omega has to choose a different prime number. Fortunately, for every prime number there exists a distinct prime number.
EDT’s policy is not “two-box if both numbers are prime or both numbers are composite”, it’s “two-box if both numbers are equal”. EDT can’t (by hypothesis) figure out in the allotted time whether the number in the box (or the number that Omicron chose) is prime. (It can readily verify the equality of the two numbers, though, and this equality is what causes it—erroneously, in my view—to believe it has control over whether it gets paid by Omicron.)