Sunday, September 28, 2008

Yet Another "Largest Known Prime Number!"

As reported by 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.

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