## New Largest Prime Number Found

February 7, 2013

A research project called the Great Internet Mersenne Prime Search (GIMPS) announced that it had discovered the largest prime number yet known. A prime number is a whole number that is only evenly divisible by itself and by 1. Familiar examples of primes include 2, 3, 5, 7, and 11. The recently discovered prime is a bit too long to write out here—it has 17,425,170 digits, which would take up several thousand pages.

However, the new prime can be written as a formula. It is equal to 2^{57,885,161} – 1. The raised number is an exponent, meaning that the number 2 is multiplied by itself 57,885,161 times. As it happens, the exponent is also a prime number, making the new prime a special kind of number called a Mersenne prime. Mersenne primes, named after the French mathematician Marin Mersenne, come in the form 2^{p} – 1, where *p* is some other prime number. There are only 48 known Mersenne primes.

Almost all of the largest known prime numbers are Mersenne primes, largely because they are the easiest large primes for computer programs to find. Even so, extremely large primes require a huge amount of computing power to discover. To speed up the process of discovery, GIMPS “crowd-sources” its Mersenne-prime-finding program by running it simultaneously on a large number of volunteers’ computers. Curtis Cooper, a professor at the University of Central Missouri, had the computer that discovered the biggest prime number yet. It took his machine 39 days of continuous calculation to find it.

The last prime number to hold the “largest” title, another Mersenne prime, was found in 2008. This latest prime number is the largest currently known, but it is certainly not the largest prime number. No such number exists—since there are infinitely many primes, a fact proven by the ancient Greek mathematician Euclid.

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