Miller-Rabin test is a primality test algorithm which determines whether a given number is prime or not. Implement Miller-Rabin primality test as given in the text book page 257, Algorithm 7.44. (aN− 1 6= 1 mod N) Write three functions to answer each of the below questions. (a) Given a positive integer N, check whether it is prime or not. 1-1• Input: N • Output: Prime or Not • For example, Input: 31 • Output: prime (b) Given a positive integer N, find the smallest prime greater than N. • Input: N • Output: M • Example: Input: 25 • Output: 29 (c) For a composite number, N = 221 (13 ×17), Miller-Rabin test outputs N = 221 as ‘prime’ for a = 174. Such a are known as strong liars. Find all other strong liars for the N = 221. Similarly, for a = 137 , it shows that N = 221 is composite. Such a’s are known as strong witness of compositeness. Find other strong witnesses if any.

prob3.py

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