Theory of Numbers

Mersenne

Marin Mersenne was a French number theorist who lived from 1588 to 1648. Mersenne attended the College of Mans, the Jesuit College, and then Sorbonne to study theology. In 1611, he joined the religious order of the Minims. Once in the order, Mersenne continued his studies at Nigeon and Meaux. He became a priest at the Place Royale. The area in Paris, where Mersenne taught, became a meeting ground for Fermat, Pascal, and others who later became the core of the French Academy. Mersenne’s involvement with other prominent mathematicians greatly contributed to the spread of mathematical knowledge throughout Europe at a time when there were no scientific journals. Mersenne’s prime research involved prime numbers.

A prime number is an integer with only positive divisors one and itself. The ancient Greeks proved that there where infinitely many primes and that they where irregularly spaced. Mersenne examined prime numbers and wanted to discover a formula that would represent all primes. The formula is (2p-1) where p is a known prime number. Mersenne claimed that if a number n=(2p-1) is prime then p=2,3,5,7,13,17,31,67,127, and 257, but composite for the other forty-four primes smaller than or equal to 257. He was wrong about five primes less than or equal to 257. He claimed 67 and 257 had a p that was prime and he also missed three that did have a p that was prime. He would never be able to accomplish the task of creating a formula to represent all prime numbers; however the form he created is still used today when searching for large prime numbers.

The largest known prime number today is (26972593-1). It was found using the format that Mersenne created over 400 years ago. The first five primes in the top ten largest recorded primes are Mersenne primes. While Mersenne objective in the prime number field failed, his work will continue to inspire research and development in the mathematical field.