Tuesday, June 26, 2007

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.


Unknown said...

Wastes of time(such as figuring out the largest prime number) should be illegal in some states.
-Andy King

Ken said...

In which states should it be illegal, my dear student?!? Thanks for reading, Andy.