Largest Prime Number Yet, Discovered

February 13, 2013 GB Math News

Even though every mathematician knows that there is no largest prime number, (for any prime number, a larger prime number exists), that did not stop some from searching for the largest prime number.

Marin Mersenne

On January 25, 2013, Dr. Curtis Cooper of the Great Internet Mersenne Prime Search (GIMPS), a professor at the University of Central Missouri, discovered the 48th Mersenne prime which is equal to $2^{57,885,161} - 1$ a number which is about 17 million digits. This the 14th score of GIMPS in discovering the largest prime number yet. It took 39 days of non-stop computing for the primality proof and it was verified by different software and hardware. Dr. Cooper won $3000 for the discovery.

For young mathematicians who are aspiring to be prime hunters, $150,000 and $250,000 will be awarded to individuals or a group who will discover prime numbers with at least 100 million digits and at least 1 billion digits respectively.

Prime numbers are positive integers that are divisible by 1 and itself only. Mersenne primes are prime numbers of the form $2^p - 1$ where $p$ is prime. The smallest Mersenne primes are