# Simanaitis Says

On cars, old, new and future; science & technology; vintage airplanes, computer flight simulation of them; Sherlockiana; our English language; travel; and other stuff

# THE 50TH MERSENNE PRIME IS FOUND!

TO PUT IT succinctly, 277,232,917 – 1 = Mersenne50! On the other hand, this might be a bit too succinct for non-math types, so let’s talk about prime numbers, Father Marin Mersenne, a special class of such prime numbers known as Mersenne Primes, a consortium of computer users, and a Memphis church deacon.

A prime number is one that’s divisible by no others than 1. The smallest ten primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29; there is no largest prime. Euclid, of geometry fame, proved there are infinitely many. What’s more, as I noted back in “Primal Fun,” primes can be thought of as the building blocks of the natural number system. They are also key to applications in digital security, cryptography, and even in cryptocurrency blockchains. Large primes, in particular, are used as stress tests for computer operation.

Father Marin Mersenne was a seventeenth-century French scholar who studied numbers, especially of the form 2n – 1, which came to be known as Mersenne numbers.

Father Marin Mersenne, 1588–1648, French polymath, priest, music theorist, composer, theologian, and mathematician.

Tantalizingly, if n is prime, the first bunch of Mersenne numbers are also prime. To wit, 22 – 1 = 4 – 1 = 3, a prime; 23 – 1 = 8 – 1 = 7, another prime. So is 25 – 1 = 32 – 1 = 31; and so is 27 – 1 = 128 – 1 = 127.

Hey, we’re onto something here! How about 211 – 1?

Drat! 211 – 1 = 2047 = 23 x 89, and hence not prime.

However, tantalizingly enough, 213 – 1 = 8191 is a prime, and so the game continues.

The University of Illinois Urbana celebrated discovery of a new Mersenne Prime in 1985. Liechtenstein celebrated another.

The discovery of increasingly larger primes has become a challenge for larger and larger computers or, equally potent, a consortium of computers.

Enter GIMPS, the Great Internet Mersenne Prime Search. Since 1996, volunteer members of this group have shared their computers’ free time searching for new Mersenne Primes.

GIMPS offers free downloading of Prime95 and MPrime, Mersenne-search software devised by George Woltman. The website also recounts the work of this consortium. Discovery of a new Mersenne Prime isn’t confirmed until subsequent computer analyses verify that it is indeed prime and that no bugs are found in its computation.

The GIMPS website also has an entertaining, no, make that hysterical video celebrating the discovery, announced on January 7, 2016, of M49, the 49th Mersenne Prime—and the largest prime of any sort discovered up to that time. M49 is 274,207,281 – 1 and has 22,338,618 digits.

Jon Pace is the discoverer of M50, the latest Mersenne Prime and, as of this writing, again the largest known prime number. M50 is 277,232,917 – 1 and has 23,249,425 digits, nearly a million digits larger than M49.

Jon Pace, Memphis church deacon, FedEx finance manager, math aficionado, discoverer of M50, aka M77232917, this latter format identifying its power of 2 before subtracting that 1.

Jon Pace’s achievement made The New York Times, January 26, 2018, in “How a Church Deacon Found the Biggest Prime Number Yet (It Wasn’t as Hard as You Think),” by Valencia Prashad.

Pace is quoted observing, “There are tens of thousands of computers involved in the search. On average, they are finding less than one [Mersenne Prime] a year. The odds of one of my computers making a prime number discovery are astronomical.”

Pace has been a GIMPS volunteer for 14 years. He keeps the Mersenne-search software running in the background of his home computers and ones at the Germantown Church of Christ, where he’s also network administrator.

On December 26, 2016, GIMPS’ George Woltman emailed Pace, “Congratulations, Jon! It’s either a new Mersenne prime (99.999%) or a ‘bug (.001%)’ ” On January 16, 2018, GIMPS confirmed the discovery.

Pace says his passion for math came from Harold Knight, an inspirational high school teacher. The New York Times quotes Pace’s daughter, Katherine, 19, saying, “The coolest thing about it is really seeing my dad’s humility on display. He is quick to tell people that anyone could have done it.” ds