Mersenne Prime Number

I just learned of a little math fact today. A Mersenne number is a number that is one less than a power of two. (*see source 1)

2^n – 1

1, 3, 7, 15, 31, 63, etc.

A prime number is a number that is only divisible by itself and the number one.

2, 3, 5, 7, 11, 13, 17… etc

By putting these two bad boys together we get the Mersenne Prime. A number that is one less than a power of two that is ALSO a prime number.

1, 3, 7, 31, 127, 8191, etc.

These Mersenne numbers are very tricky to figure out. In fact, there are only 44 that have ever been discovered; the largest having over 9.8 million digits in the number (2^32,582,657 – 1). One cool thing about Mersenne Primes is that always is the case where two must be raised to the power of a prime number. That makes hunting Mersenne Primes a heck of a lot easier though still way too hard for Windows Calculator. Also cool is that the 44th Mersenne number is currently the largest prime number known. (*see source 2)

Anyway, the exciting news of the day is that the 45th Mersenne Prime number may have been discovered!!! Hot Diggidy! Get out your party pants!! If the number confirms in September we should have a Prime Party. This one will most certainly be more than 10 million digits long which means that the GIMPS folks may win the Electronic Frontier Foundation’s prize of $100,000. And if you’re feeling ambitious, try and grab the next prime number in the list to win $150,000 or $200,000!!!! (*see source 3)

A couple sources:
1. The fast, the easy, the wikipedia
2. GIMPS – with lots of history and fun facts.
3. The Electronic Frontier Organization

4 thoughts on “Mersenne Prime Number

  • 8/31/2008 at 11:27 pm

    That party may have to go bicoastal!

  • 9/10/2008 at 10:23 am

    Some species of cicada emerge from the ground only after 13 years, and some emerge only after 17 years. Both of these are prime numbers. This means that a predator cannot become adapted to preying on cicadas as a food source very easily. For example, a cicada with a 15-year life cycle could be preyed upon by a predator with a three- or five-year life cycle, but the 13- and 17-year cycles allow them to stop the predator life cycle from synchronizing.

  • 9/10/2008 at 10:25 am

    Disclaimer: I read that on the internet so it must be true/lies*.

    (* Delete as appropriate)


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