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Ready For Prime Time: A Number With 20 Million-Plus Digits

A computer registered the current largest prime in September, but such numbers are considered "discovered" only when a human notices.

The largest-ever prime number has been discovered in Central Missouri — and oh, what a number it is.

274,207,281-1=The record number

The record number, nicknamed M74207281, has more than 20 million digits. That's nearly 5 million digits longer than the previous record. If you printed each digit 1 mm wide, the number would stretch for more than a half marathon's 13.2 miles. Or as standupmaths reports, we're talking about 2,567 killer whales stretched out end-to-end.

So how can a number be "discovered"? It happens when a human notices.

We've known for 2,000 years that there are infinitely many prime numbers (numbers divisible only by 1 and themselves). The Great Internet Mersenne Prime Search (known as GIMPS) has thousands of volunteers running searches on their computers, looking for rare, large prime numbers.

The volunteers, who join by downloading and running free software, can also win a cash prize for any discovery.

GIMPS has been working since 1996, and has discovered 15 rare prime numbers called "Mersenne primes."

These are primes that can be reached by the formula "2P-1," and they have been "central to number theory since they were first discussed by Euclid about 350 BC," GIMPS says.

And what do you do with one when you find it?

Generally, these volunteers are looking for prime numbers because they are the "key" to certain kinds of cryptography — referred to as public-key encryption.

If you want to dive into the math behind primes and encryption, the University of California, Berkeley's math department explains it in detail here. Generally speaking, this encryption scheme works because it is easy to multiply two prime numbers together — but if you're a hacker, it's much more difficult and time consuming to work backward and find what those two numbers were.

However, GIMPS acknowledges that the record prime "is too large to currently be of practical value."

The number was discovered by Curtis Cooper, a professor at the University of Central Missouri, and then independently verified.

It's the fourth time Cooper has discovered a record prime — but he says the magic hasn't worn off. "I think I still have the same excitement as when we were lucky enough to find the first one," he tells standupmaths.

The big discovery almost slipped through the cracks, he says. The machine is supposed to automatically notify the team when it finds a new prime — but that email never came. The number was found during routine database maintenance, nearly four months later.

Curiously, Cooper says that the computer's notification system also failed the four other times it found a record number.

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