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We Have A New Prime Number, And It’s 23 Million Digits Long

Somewhere out there on the number line, huge prime numbers are lurking, waiting to be discovered. On Wednesday, a new one was. The Great Internet Mersenne Prime Search, an organization devoted to doing exactly what its name suggests, announced that it had discovered a new prime number, the largest ever found: \(2^{77,232,917}-1\). That’s more than 77 million 2s all multiplied together, minus 1. I’d write it all out for you, but there’s a big problem: It’s 23,249,425 digits long. (So, it goes by its nickname: M77232917.)

Instead of writing it out, I’ll offer this chart, which shows how long the longest known prime has been over time. (We’ve charted it on a log scale so we can more easily compare the huge range of numbers.)

A prime number is a number that is divisible only by itself and one. These numbers play an important role in pure mathematics and its field of number theory. Emphasis on pure. The British mathematician G. H. Hardy once proudly wrote that number theory was so free of practical application that “no one has yet discovered any warlike purpose to be served by the theory of numbers.” (That has changed recently, however, as primes now play an important role in cryptography.)

Mathematicians have been searching for primes for centuries, often with no more than a quill and a brain. By 1588, an Italian mathematician had proved that 524,287, or \(2^{19}-1\), was prime. By 1772, the legendary Leonhard Euler had shown that 2,147,483,647, or \(2^{31}-1\), was, too.

Then came the computer. You can clearly see the dawn of the computer age in the chart above. Over the course of the past 70 years or so, the longest known prime has become thousands and thousands of times longer. Supercomputers have been a boon for prime hunters. The discovery of longer primes has gone hand in hand with the development of faster and more powerful processors.

Today, the Great Internet Mersenne Prime Search project relies on distributed computing to hunt its mammoths. As with similar projects for folding proteins or searching for extraterrestrials, volunteers download custom prime-searching software and donate their spare computing power to the project. One such volunteer, Jonathan Pace, discovered M77232917 on his machine the day after Christmas. He’d been searching for 14 years. It took six days to prove that the number was indeed prime.

M77232917 is certainly not the largest prime number. In fact, there is no largest prime number. There are infinitely many — a fact established by the Greek mathematician Euclid around 300 B.C. Fascinating open questions about prime numbers do remain, such as the Goldbach conjecture (which wonders if every even integer above two can be expressed as the sum of two primes) and a twin prime conjecture (which wonders if there are an infinite number of pairs of primes separated by 2, like 11 and 13).

But finding an even more enormous prime won’t prove these mathematical ideas. So why hunt? Reasons provided by the prime search project include tradition, collection, glory and money. It lists a $250,000 prize for the first billion-digit prime. Happy hunting.

Oliver Roeder is a senior writer for FiveThirtyEight.

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