Optimal prime

Over 2000 years ago, Euclid of Alexandria proved that there are an infinite number of prime numbers, and ever since, mathematicians have worked to identify larger and larger examples. Since 2008, the biggest known example was a number over 13 million digits long. But now that record has been smashed, with a computer in Missouri calculating a prime an incredible 17 million digits long – so long that if you started writing it at a pace of two digits every second, it would take 101 days to complete and fill over 5500 sheets of A4 paper!

A prime number is any number divisible only by itself and one. So, 7 is a prime number because its only divisors are 7 and 1, but 8 is not, because it can be divided by itself, 4, 2 and 1. This new record holder, 2^57,885,161 -1, is a special type of prime called a Mersenne prime, named after 17^th century monk Marin Mersenne. A Mersenne prime can be written as 2^p-1, where p is also a prime number, and only 48 examples have been identified thus far. The latest was discovered by mathematician Curtis Cooper of the University of Central Missouri, as part of the Great Internet Mersenne Prime Search project (Gimps). Gimps has been running since 1996, and involves tens of thousands of computers in multiple locations, all focusing their considerable computing power on the hunt for massive primes.

While discovering a new prime does not have much practical use, mathematicians continue the search for other reasons, with Cooper telling the Associated Press: “I kind of consider it like climbing Mount Everest or finding a really rare diamond or landing somebody on the moon. It’s an accomplishment. It’s a scientific feat.” And there are other benefits too: Curtis will receive $3000 for this particular breakthrough, while the Electronic Frontier Foundation are offering cash prizes to the mathematicians who first identify prime numbers that are 100 million digits long and 1 billion digits long – milestones that will net their discoverers $150,000 and $250,000 respectively. But the biggest jackpot is reserved for the person who manages to definitively explain the pattern of primes. The Riemann Hypothesis, first proposed in 1859 by German mathematician Bernhard Riemann, indicates such a pattern, and if you can mathematically prove it will always hold true, you’ll receive $1 million for your efforts!