# New “largest” prime number discovered!

February 5, 2013 2 Comments

Hold on to your hats! A new “largest” prime number has been discovered. Meet

**2 ^{57,885,161} – 1 **

How large is it? Try to imagine this … a whopping 17,425,170 digits! (Click here to see most of the number.)

This number is a special kind of prime number, called a Mersenne Prime. First popularized by the French monk Marin Mersenne, primes of this form are generated using the formula 2^{p} − 1 (where p is prime). For example: if p = 2, then 2^{2 }– 1 = 3 or if p = 5, then 2^{5 }– 1 = 31. And, as you know, both 5 and 31 are prime numbers.

I know what you are thinking – I thought it was impossible to have a formula that generates primes. Well, yes and no. While there is no formula that will generate ALL prime numbers, there are many formulas that generate some primes. Unfortunately, as with all prime formulas, even this formula doesn’t always work. For example, if p = 11, then 2^{11 }– 1 = 2047. 2047 is a composite number with factors 23 and 89.

So, why bother with a formula that inconsistently generates primes? Well, mathematicians are fun people. And, like most people, they are attracted to big things – like big prime numbers. Since this formula can generate some pretty massive numbers, the potential for monstrous-sized prime numbers exists. And, what’s better than massive prime numbers? Nothing! In fact, some mathematicians are so obsessed with really big primes that they have started an internet search for big primes called GIMPS – the Great Internet Mersenne Prime Search.

And, now, thanks to the GIMPS project, we have the 48th Mersenne prime … all 17,425,170 glorious digits.

Click here for the official press release.

2,047 = 23 x 89 🙂

Good call! I fixed it. Thanks for noticing.