using either the grade school algorithm for multiplication or the Karatsuba algorithm, How much time would be required (on a single machine) to prove the primality of the 49th Mersenne prime? ( Proceed by making some reasonable assumptions about the recurrence expressing the running-time of both multiplication methods and solving them. )

Count time for subtraction to be the same as addition and the time for modulo (%) to be the same as multiplication.

additional info:

On January 19, 2016, Dr. Curtis Cooper published about his recent discovery of a 49th Mersenne prime, 274207281 - 1 (a number with 22,338,618 digits), as a result of a search executed by a GIMPS server network. The best method presently known for testing the primality of Mersenne numbers is the Lucas-Lehmer test. Specifically, it can be shown that for prime p > 2, Mp 2p -1 is prime if and only if p- 1 is (Sp-2) 96 M,-0, where So = 4 and, for k > 0, Sk = ((Sk-1)2-2) 96 Mr