Gap problems; Hardness of Gap-Problems implies Hardness of approximation. Applied to E4SAT. 9 June 30, July 1 Primality testing: groups and subgroups, Fermat's test , Carmichael numbers, fast exponentiation, Miller-Rabin test.   July 1 Randomized Algorithms: Karger's algorithm for MIN-CUT [MR1.1] ; Every graph has O(|V| 2 ) minimum cuts. 10