III. Results

The results we obtained for our Mersenne prime number generator were better than we first predicted. The time it took to generate the prime number 2^{21701}-1 took only 29.92 seconds of processor time on Pi and, as the charts indicate, only 2.82 seconds on Rho with the 50,000-unit array. When we tested the generator on a Pentium-133, the processor time was only 1min 58sec.
Of course, Rho is better equipped for large number calculations than Pi or a desktop computer and therefore the processing time is significantly less. We also discovered that it is important, in order to maximize efficiency, to make the number of cells in the array as close to the number of digits in the prime being generated. This cuts down on the number of cells that are not being used, but must be included in the processing. Rho takes 2.2 seconds less processor time to generate a 6,533 digit number when the array is 7,500 units long than if the array 50,000 units long. Pi takes a full 20 seconds less processor time.
Once we finished our number-generating program, we planned on importing the now accurate Mersenne number into our factorization code to verify that it is prime. We ran into our original problem, however, of the program not working for numbers above the ninth prime, or 2^{61}-1. We sent the output of the factorization of the Mersenne Number 2^{21701}-1 to a file. The printed output is Appendix B.