## Prime Numbers

Great News! A new prime number was discovered and announced on February 5, 2013, consisting of over 17 million digits! What, you don’t share my enthusiasm? Oh, I see, it’s perfectly fine to act like a hyper-caffeinated baboon at a sports event but not to get excited about the first prime number discovered in four years? Seriously, folks, if 2^{57,885,161} – 1 = 581,887, …, 285,951 doesn’t move your mojo then why don’t you just pull up a rocking chair to your front porch and spend your remaining days waving to cars as they drive by. By the way, to see all 17,425,170 digits (which I highly recommend) please visit http://www.isthe.com/chongo/tech/math/digit/m57885161/prime-c.html.

So, why all the excitement? Because…well, because it’s there! Finding prime numbers is the mathematical equivalent of climbing Mt. Everest, except that it’s safer and can be done indoors. Sometime around 300 BC Euclid (yes, the same guy that Euclidian or plain geometry is named after) proved that there is an infinite number of prime numbers. So you see, the fun never ends! Another year, or two, or three, and the good folks at the Great Internet Mersenne Prime Search (GIMPS), a computer program that networks PCs worldwide to collectively hunt for prime numbers, will thrill us all once again, and again, and again…with yet another prime number!

What’s a prime number, you ask? It’s a whole number (positive integer) greater than 1 which is divisible only by one and itself. The first four prime numbers are 2, 3, 5 & 7. Prior to use of computer systems finding the next highest prime number was an arduous, yet rewarding, task. In fact, the last largest known prime number prior to the development of the digital computer was found in 1871, 2^{127} – 1, a mere 39 digits long. Beginning in 1951 prime numbers have been generated using digital computers. In 1997 GIMPS was founded and to date the project has generated fourteen Mersenne prime numbers, culminating in the latest one and the subject of this blog—and my excitable state at the moment (I’m sure the espresso I just had contributed to my euphoria).

What’s a Mersenne prime number you ask (assuming you have not yet hit the “back” button on this blog)? It’s the discovery of a 17^{th} century French monk of the Order of Minims by the name of Marin Mersenne (pictured at the top of this blog). He was one of the most prominent mathematicians of his day and a contemporary of the likes of Galileo, Descartes and Pascal. Mersenne, like many other monks throughout the history of Christianity (e.g., 15^{th} century Franciscan Friar William of Okkam, “Okkam’s Razor” and 19^{th} century Augustinian Friar Gregor Mendel, “father of modern genetics”) puttered with all sorts of science stuff. You might say that this was their way of “*monk-eying around*” (am I hilarious or what?).

In Mersenne’s case he dabbled into mathematics and physics. For instance, he studied the oscillation of the strings of acoustic instruments and derived the mathematical formula for the musical notes they produce. But Mersenne is best known for his discovery of the *Mersenne primes*. He attempted to find a formula for finding all prime numbers—but failed (so has everyone else since, by the way). Instead, he discovered that some prime numbers have the form,

*2 ^{p} – 1, where p is a prime number*

But not all, for instance, 11 is a prime number, yet

*2 ^{11} – 1 = 2047 = 23 X 89*

Sad. But the good news—and this is where it really gets exciting—is that it has been proven that if a prime number is a *Mersenne prime* (i.e., the result of *2 ^{p} – 1)*, then

*p*must be a prime number. And although no general algorithm for determining prime numbers has yet to be discovered, we can sleep at ease tonight knowing that the Mersenne prime number formula helps us eliminate many would-be impostors.

OK, OK, this blog is about as useful as a screen door on a submarine. Regardless, it needed to be posted simply...because it was.

God bless!

*CalvinCuban*