## February 6, 2013 9:25 am

### How Do You Discover a 17 Million Digit Prime Number?

The beginning of the largest prime number ever discovered. Image: Mersenne.org

You probably remember prime numbers from school. They’re numbers like 2, 3 and 17, which are only divisible by themselves and one. But the prime numbers you learned in school are puny compared to the most recently discovered one. The 48th Mersenne prime was recently discovered on the computer of a man named Dr. Curtis Cooper, and it’s 17 million digits long. Ars Technica reports:

The 48th Mersenne prime was discovered as part of the Great Internet Mersenne Prime Search (GIMPS), a project that has used volunteer computers to calculate and search for primes for 17 years. Dr. Cooper’s computer took 39 days of continuous calculation to verify the prime status of the number, which has over 17 million digits and was discovered January 25. GIMPS’ algorithm was developed in the early 1990s by Richard Crandall, an Apple Distinguished Scientist.

What is a Mersenne prime, anyway? Mersenne.org explains it this way:

A Mersenne prime is a prime of the form 2P-1. The first Mersenne primes are 3, 7, 31, 127 (corresponding to P = 2, 3, 5, 7). There are only 46 known Mersenne primes.

Ars Technica writes that among the numbers between 0 and 225,964,951-1, there are 1,622,441 prime numbers. Within that same range, there are only 42 Mersenne primes. That’s how rare a Mersenne prime is.

The interesting thing about finding Mersenne primes is that it’s really not possible without a computer. Notice how Dr. Cooper didn’t really discover the number; his computer did. That’s what Mersenne.org does—help people search for primes. The Great Internet Mersenne Prime Search (GIMP for short) has been going on for 17 years. The current form of the program that helps people search was developed by Richard Crandall in the early 1990s. It essentially searches for a prime number and then verifies that the discovered prime is, in fact, prime.

Then, the number had to be re-verified, which took another set of computers. Mersenne.org describes the process this way:

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 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.

For his time and computer work, Dr. Cooper will get \$3,000. This is the third prime discovery for Dr. Cooper, and those who want in on the hunt (and potential cash) can download the program and run it on their computers. Essentially, a complete math novice can find the largest prime number in the world.

More from Smithsonian.com:

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