Yet Another "Largest Known Prime Number!"

As reported by foxnews.com and elsewhere, researchers at UCLA have discovered the "newest" largest known prime number, a behemoth with nearly thirteen million digits. It is called a Mersenne prime, after a French mathematician who discovered this particular class of prime numbers. It is found by taking "2" to the power of 43,112,609, and then subtracting "1".

Prime numbers are numbers like 2, 3, 5, 7, 613, 1999, and others which have only two whole-number factors: 1 and itself (View the first 1000 prime numbers here). As numbers get higher, "testing" a number to see if it is prime gets increasingly time-consuming. But mathematicians have also proved (in a manner beyond what most readers care to know) that there cannot be a largest prime number; in other words, there are infinitely many prime numbers. Therefore, there is a certain sense of accomplishment to finding yet another "largest known prime."

A few interesting facts about this number:

• It can be shown (using logarithms) that this number actually has 12,978,189 digits.
• If the number were written out, using 16 digits per inch, the number would be 12.8 miles long. In metric, if we use the even-smaller 1 digit per mm, the number would be nearly 13 kilometers long (just over 8 miles).
  
• 75 computers in a network, using Windows XP, were harnessed to do the raw calculations.

And, believe it or not, once it is verified, the UCLA folks win a $100,000 prize for finding the first known prime number exceeding 10,000,000 digits. (Did you notice that they win ten million pennies' worth of money?)

I actually blogged on this topic last year, too.

What is the largest known prime number?

Most of you are aware of the existence of something called prime numbers: Numbers having only two proper factors, which are the number itself, and one. Examples of prime numbers include 2 (the smallest), 3, 5, 101, 2003, and the 110-digit number 3520154665960884202608832800756586623196257878464375664- 7773109869245232364730066609837018108561065242031153677.

Mathematicians have been able to prove that there is NO "largest prime number," so the contest turns to the question of what is the largest known prime number. And don't think that there aren't some competitive math types out there looking for it, with multiple supercomputers that take months to determine such things.

The current "winner" is the number formed by taking 2 to the power of 32,582,657 [that's 2 x 2 x 2 x 2 x 2.....but with 32,582,657 2's in the list] and subtracting 1. This number, when properly calculated, contains 9,808,358 digits. You can read more about it at http://www.mersenne.org/, and if you don't feel like waiting for your computer to print it [Note: I can print one page with 3588 digits, in Times New Roman (12 point), using 1" margins all around. At that rate, you would need 2734 sheets of paper], you can order the poster at http://www.perfsci.com/souvenirs.htm. Really. $94. All 9,808,358 digits, in something like 1-point font...and they also sell a watchmaker's loupe so that you can read the 29"x40" poster.