Problem 10. Prime factorization timing. (10 pts) To get a feel for how difficult it is to factor numbers that are the products of large primes, we will use the "Prime Factorization Machine" in the lab to factor some large numbers. First try three numbers (not too large - say, 8 digits at most) that you make up yourself, by multiplying several small prime numbers on your calculator, and check that the "Factorization Machine" gives the right answer: Answer: Note that the "Factorization Machine" doesn't only factor; it also computes how much computation time it took to carry out the factorization. Now use the "Factorization Machine" to factor following numbers, and write down how long it takes your computer to factor them. If takes longer than a couple minutes to factor one - do not attempt to factor the next number in the series. Based on these timings, estimate how long it would take to factor a 155 digit number. Describe how you obtained you answer. Answer: 1407673 took milliseconds. 13309117 took milliseconds. 137937281 took milliseconds. 1438671211 took milliseconds. 14698154927 took milliseconds. 135677280727 took milliseconds. 1389864140741 took milliseconds. 13472900573921 took milliseconds. 130062255272767 took milliseconds