IV. Conclusion

When Mersenne first published his results for the eleven prime numbers he found, he most likely did not foresee the frenzy the discovery of each new Mersenne prime causes. The possible applications of these huge prime numbers continues to grow with the numbers. It is the Mersenne Prime that will continue to be tested because it can be represented simply. 2^{n}-1 is much easier to represent than a number that is 100 pages long. Among the several methods of testing, the simple trial-and-error method works better than complex algorithms that eat up massive processor time. It was our hope to discover a new prime number, not necessarily the largest, but one that had not been recognized previously.
Although we were not successful in finding a new prime number, it is clear that we achieved our next goal of testing computer efficiencies. As the charts clearly show, the processor time increased dramatically from Rho to Pi to A Pentium-133, and there was another jump as we streamlined our code to an array that was just over the size of the number we were generating. This type of testing shows that accuracy and speed can be quantitatively tested for anyone who needs to do large number calculations through a simple program.