4. You have an idea for a faster program. You scour the Internet and, as luck would have it, you find an algorithm one prime factor(N) that, given an n-digit binary number, N, will find one prime factor of the number in e(n?) (a) Using this algorithm (as a black box), give an efficient algorithm to factor an n-digit binary number into primes and print the prime factors). (b) Approximately how many times does your factoring algorithm use the one prime factor (N) routine in the worst case, as a function of n? (c) How fast is your algorithm (in the worst case), in order notation, as a function of n? As above, assume that it takes linear time, i.e. e(n) time, to add, subtract, multiply, and divide two n-digit binary numbers. (d) Is your new program fast enough? Justify