The man behind the Mersenne primes

On September 3, 1996, the 34th known Mersenne prime – 2^1257787 - 1 – was discovered by mathematicians David Slowinski and Paul Gage. This is the largest Mersenne prime number so far to have been found without the involvement of the Great Internet Mersenne Prime Search, which has been involved in all Mersenne prime discoveries since then. A.S.Ganesh takes a look at Mersenne primes and the man who lends his name to these primes…

You know what prime numbers are, don’t you? A whole number greater than 1 that has no factors other than 1 and itself is referred to as a prime number. These numbers have been known and researched for a long time and are intertwined with our lives in more ways than we can imagine.

Prime numbers of the form 2n-1 are referred to as Mersenne primes. Mersenne primes have become extremely popular as the largest known prime numbers are all of this type. This has even led to the creation of an active programme to find out more Mersenne prime numbers.

This distributed search programme across the internet, known as GIMPS (Great Internet Mersenne Prime Search), sees hundreds of volunteers pitch in to perform pieces of this search by employing their personal computers. As a result of this voluntary programme, every Mersenne prime discovered since late in 1996 has GIMPS as a discoverer.

There are 51 known Mersenne prime numbers so far. Every one of them from the 35th has GIMPS as one of the discoverers. Additionally, GIMPS participants have tested and verified all exponents below 5,33,10,629 and tested all exponents below 9,17,65,997 at least once as of September 2020.

In case you are wondering where the ‘Mersenne’ comes from, it belongs to a French polymath called Marin Mersenne. While Mersenne is best recalled for the primes that now bear his name, his significance stems from other areas too.

Born near Oize, Maine, France on September 8, 1588, Mersenne was educated at the Jesuit College of La Fleche soon after it was founded in 1604. By 1609, he had left La Fleche to study theology in Paris, both at the Sorbonne and the College de France.

At the age of 24, Mersenne joined the austere Roman Catholic Order of Minims. Barring the years 1614-18 when he taught philosophy and theology at Nevers, Mersenne spent most of his life until his death in 1648 living in Paris.