Mathematicians Just Found A New Prime Number — With 17 Million Digits

An Internet search team looking for ever more prime numbers has broken their four-year dry spell and just announced that they found a new one — with 17 million digits. I can’t write out those digits for you, but here’s the short hand: 2 ^ 57,885,161 minus 1.

For those not in the maths know, a prime number is a special kind of number that can only be divided by itself and one. The search party, called the Great Internet Mersenne Prime Search, is actually searching for an even more unique number — a special kind of prime number called a Mersenne prime, a prime number that can be written in scientific shorthand 2p – 1, where the exponent is itself a prime. In this example, 57,885,161 is the prime exponent.

This new number is only the 48th Mersenne prime ever found. It’s also the biggest. The second largest Mersenne prime has just under 13 million digits. Here’s how they do it, explained by Jacob Aron of New Scientist:

Though there are an infinite number of primes, there is no formula for generating these numbers, so discovering them requires intensive computation. GIMPS uses volunteers’ computers to sift through each prime-number candidate in turn, until eventually one lucky user discovers a new prime.

… Though there is little mathematical value to finding a single new prime, these rare numbers are prized in their own right by some. “It’s sort of like finding a diamond,” says Chris Caldwell at the University of Tennessee, Martin, who keeps a record of the largest known primes. “For some reason people decide they like diamonds and so they have a value. People like these large primes and so they also have a value.”

After the discovery, it took 39 days of calculations to prove the number was a Mersenne prime.

Prime numbers are also important in cryptography, which is used to make online transactions secure.

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