# Largest Prime Number Discovered

Back when I was in college, I participated in the great GIMPS Project, searching for what is known for a Mersenne prime number (Mersenne primes are of the form (2^X)-1, with the first primes being 3, 7, 31, and 127 corresponding to X = 2, 3, 5, and 7, respectively). My computer would use its extraneous resources to help in the search, and while nothing ever came of it, it’s pretty cool to know that I made a modest contribution to the project. So it was great to learn today that the GIMPS Project found the largest prime number ever as of January 2013. The largest (known) prime number now is 2^57,885,161-1, and its discovery is noted on this post:

The new prime number is a member of a special class of extremely rare prime numbers known as Mersenne primes. It is only the 48th known Mersenne prime ever discovered, each increasingly difficult to find. Mersenne primes were named for the French monk Marin Mersenne, who studied these numbers more than 350 years ago. GIMPS, founded in 1996, has discovered all 14 of the largest known Mersenne primes. Volunteers download a free program to search for these primes with a cash award offered to anyone lucky enough to compute a new prime. Chris Caldwell maintains an authoritative web site on the largest known primes as well as the history of Mersenne primes.

To prove there were no errors in the prime discovery process, the new prime was independently verified using different programs running on different hardware. Serge Batalov ran Ernst Mayer’s MLucas software on a 32-core server in 6 days (resource donated by Novartis[2] IT group) to verify the new prime. Jerry Hallett verified the prime using the CUDALucas software running on a NVidia GPU in 3.6 days. Finally, Dr. Jeff Gilchrist verified the find using the GIMPS software on an Intel i7 CPU in 4.5 days and the CUDALucas program on a NVidia GTX 560 Ti in 7.7 days.

This largest prime number contains 17,425,170 digits. If you have a fast Internet connection, you can see how huge this number is (with all of its digits written out one by one) by clicking here. Pretty cool.

## One thought on “Largest Prime Number Discovered”

1. It make’s me want to look at the research more, I mainly focused on numerical analysis in college. I know just before I left last year there were several papers that were said to make a good contribution to FFTs. Though the main help to the computational complexity is up to the parallel algorithm implementation and that’s messy. The verification across different architectures and software was good, hopefully leads to better design and implementation.