## New Largest Known Prime Discovered

posted about 10 years ago

A new prime has been found, taking two rather interesting titles. First, it's now the largest known prime. That's cool, right? But even cooler is that this new prime is the 48th known Mersenne prime. Mersenne primes take the form (2^p)-1, where p itself is a prime. That is, Mersenne primes are primes that are one less than a power of 2. The list begins with 3, 7, 31, 127, ... It is not known if there are infinite Mersenne primes or not.

This prime is (2^57,885,161)-1, which is 17,425,170 digits long. Typing this out in MS Word using the standard font size (TNR, size 12, default margins) would result in a 5000+ page document.

Mersenne primes are neat not just because of their form, but because they are related to perfect numbers. If M is a Mersenne prime, then M(M+1)/2 is a perfect number. Perfect numbers are numbers that can be expressed as the sum of their proper positive divisors (its divisors, not including itself). This list begins as 6, 28, 496, 8128, ... The proper positive divisors of 6 are 1, 2, 3, which add up to make 6.

The prime was found via the Great Internet Mersenne Prime Search (GIMPS). This utilizes the computing power of a network composed of volunteers in order to find more Mersenne Primes.