A Mersenne Prime is a type of prime number of the form 2n - 1, where n is also a prime number . While seemingly simple, this formula of 2n - 1 has consistently produced the largest prime numbers in the world. The current largest prime number, 282,589,933 - 1, is a Mersenne Prime and has 24,862,048 digits . While Mersenne Primes seem like they serve little use aside from being astoundingly large numbers, massive prime numbers actually have many uses especially for cryptography and information technology . Finding new Mersenne Primes has been a goal of the mathematics community for centuries, with the origins of Mersenne Primes dating back to 1536. Currently the search for prime numbers has led to some major advancements in the field of distributed computing.
Currently there have been 51 Mersenne Primes identified, with the last 17 Mersenne Primes having been discovered by the Great Internet Mersenne Prime Search (GIMPS) . GIMPS is one of the largest distributed computing projects in the world. Volunteers sign up and download the GIMPS software to their machines. The GIMPS software then runs in the background of every volunteer’s computer looking for large primes and reporting its findings. The GIMPS software is specially built to be hyper efficient for finding large Mersenne Primes and is not a general purpose prime finding software.
Motivations and Methodology
Rather than trying to outperform GIMPS, the scope of this project was narrowed down to using a Mersenne Prime search as a tool for benchmarking different tools created by Distributive and demonstrating the potential for distributed computing to tackle cutting edge problems. Four methodologies were employed in this project, two conventional approaches to the problem and two distributed computing approaches to the problem.
Approach 1: Python is one of the most popular coding languages especially for computation and data analytics. Python is one of the most accessible languages and gives users the ability to create powerful programs with relatively little programming experience. Its main issue is that it is a computationally slow language.
Approach 4: Bifrost is a tool built around DCP that allows users to write Python code and run that code through the DCP protocol. This makes creating code for DCP much easier as Python is generally considered a more accessible language, while still allowing users to harness the power of distributed computing. Bifrost is slower than DCP because it has to set up an environment where it can run Python code.
For each approach, multiple runs of the prime searching program were completed with each run being timed and recorded. The parameters of each run would change between runs with the amount of numbers being investigated for primality changing. The range of numbers being investigated spanned from n=0 to n=10000 in 2n -1. Data on the time until completion for each approach was collected and plotted.
Conclusion and Future Work
 GIMPS, “Great internet mersenne prime search - primenet,” 2^P-1. [Online]. Available: https://www.mersenne.org/.
 J. Palca, “The world has a new largest-known prime number,” NPR, 21-Dec-2018. [Online]. Available: https://www.npr.org/2018/12/21/679207604/the-world-has-a-new-largest-known-prime-number.
 B. Smith, “This is how prime numbers keep your online shopping secure,” ABC News, 19-Jan-2018. [Online]. Available: https://www.abc.net.au/news/science/2018-01-20/how-prime-numbers-rsa-encryption-works/9338876#:~:text=The%20reason%20prime%20numbers%20are,17%2C%20or%20187%20and%201.