# Largest Prime Number Found, with 17,425,170 Digits!

Feb 08 2013

Just a couple of weeks ago, a new prime number was found by computers: this is 257,885,161 – 1, a number with more than 17 million digits. Wow!

Known as a Mersenne prime, which is a prime number of the form Mp = 2p – 1, this latest discovery is the 48th. For such primes, p is also prime; but not all prime p‘s yield Mersenne prime numbers. For example, 211 – 1 (=2047) is not prime even though the exponent 11 is prime, since 2047 is divisible by 23 and 89. Sounds confusing? Head over to wikipedia to learn more about this topic.

Mersenne primes can be regarded as “beautiful” numbers since they are closely related to perfect numbers. We talked about this previously in our post “The Beauty of Perfect Numbers“. Basically, each Mersenne prime produces a perfect number, computed from (2p – 1) x 2p-1. Very interesting, indeed.

Looking for large prime numbers of such magnitude is a daunting task which requires clever computer programming and lots of CPU power. If you are intrigued by how computers are making such finds, discover how volunteers are using their PCs to help at the Great Internet Mersenne Prime Search (GIMPS) website.