We consider the set of prime numbers P rim, but not unary, but binary coded. Obviously, the complement of this set is in NP. Show that P rim is also in NP. Note: Use the following number-theoretic characterization cleverly out. p is prime if and only if the following is true: there is an x with 0 x p so that x p1 1 mod p, x i 1 mod p for all 1 i p 1.