A lower bound for primality (Q5943093)

The main result of the paper is that primality testing, gcd computation and square-free computation is not in \(AC^0\), that is, can not be accomplished by constant depth, polynomial-size circuits of AND, OR and NOT gates. The technique used by the authors is to reduce the functions that have circuit lower bound known to divisibility and then, using a randomized reduction, to primality testing.