The challenge of finding the largest prime number ever known seems like an impossible task, however, when you put mathematicians and 100,000 computers together, you get an amazing result, which could qualify for the $100,000 prize offered by the Electronic Frontier Foundation for the first individual or group who discovers a prime number with at least 10,000,000 decimal digits.

On August 23rd, UCLA scientists announced the discovery of a huge prime number, the world’s 45th known Mersenne prime: 2^43,112,609-1, which is basically a 12,978,189-digit number. According to the Great Internet Mersenne Prime Search (GIMPS), the UCLA Mathematics Department will receive $50,000 of that prize, $25,000 will be donated to charity, while the rest will go to discoverers of the previous six Mersenne primes.

Less than two weeks after the UCLA discovery, Hans-Michael Elvenich in Langenfeld near Cologne, Germany, found the world’s 46th Mersenne prime number, with “only” 11,185,272 digits. These discoveries have been made possible by the 100,000 computers in GIMPS PrimeNet, capable of performing 29 trillion calculations per second.

For those wondering what is a Mersenne prime, it is a number which looks like this: 2ⁿ-1. These numbers are quite controversial, since no one knows if there are indefinitely many Mersenne primes. Furthermore, the challenge of finding more Mersenne primes is even greater if we take into consideration the fact that the mysterious “n” is not necessarily a prime number.

This is the place where paper calculations need to be replaced with computer ones, since it has been proven that Mersenne primes grow very fast. Another interesting side to these numbers is that they can be written in a compact form (2ⁿ-1), without having to write all its millions of digits.

The numbers got their name from Marin Mersenne, 17th century French philosopher and mathematician, who was better known for his extensive collaboration with scientists all over the world, as well as a series of philosophical and theological writings. Mersenne compiled a list of Mersenne primes with exponents up to 257, although it is far from being completely accurate.

Ancient Greek mathematicians are the first to have presented interest in some of these numbers, and they are also the first to have found the first four of them: 2, 3, 5, and 7. Just to give an example on how these numbers grow so rapidly, while the 14th Mersenne prime is 607, the 15th is 1,279; while the 20th Mersenne prime is 4,423, the 21st is 9.689; while the 28th Mersenne prime is 86,243, the 29th is 110,503.

So far, scientists have only managed to come up with 46 Mersenne primes, however, the search continues, and whether the next one to be discovered will be smaller than 43,112,609 (the 46th in length) or will have even more digits than the 12,978,189 ones reported by UCLA, it’s impossible to say.

GIMPS will continue its quest to find the next longest Mersenne prime, and has announced that the last two discovered Mersenne primes will be printed by Perfectly Scientific, the company that developed the FFT algorithm used by GIMPS, although they did warn enthusiasts should prepare their magnifying glasses to read the tiny print.