New Largest Prime Number Discovered

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The record for the largest discovered prime number has fallen for the first time in nearly three years. The new largest runs to 22 million digits, five million more than the previous record.

The number in question is 274,207,281-1 (known also as M74207281) and, as is often the case these days, was discovered through the Great Internet Mersenne Prime Search, which uses a network of computers provided by volunteers.

A Mersenne prime is one that is exactly one less than a factor of two. Hunting for them is a simple process, but one that requires great computing power with numbers of this size. It simply involves taking every factor of two, subtracting one, then checking for any divisors that disqualify it from being a prime. For example, 22 -1 is 3, which is prime. 23 – 1 is 7, which is also prime. However 24 -1 is 15, which isn’t prime because it can be divided by 3 and 5. That means the next Mersenne prime is instead 31.

The newly discovered number is the 49th known Mersenne prime. It’s likely that most if not all largest discovered primes will continue to be Mersenne primes simply because looking for them is a much quicker process than examining every possible number one by one.

While the checking process is completely computerized, the convention is that the discovery is considered to take place when a human being first becomes aware of the number. That’s created a quirk in this case as the computer that¬†found and confirmed that M74207281 was the new record holder sent an email report to the project’s central server on September 17 last year, but the email went undelivered. The official discovery date is thus January 7 this year when the computer’s owner Curtis Cooper noticed the report as part of database maintenance.

A similar incident took place in 1961 when a computer discovered two Mersenne Primes known as M4253 and M4423 in short succession. However, the first human to read the resulting report printout did so in reverse chronological order, thus reading about M4423 first. That meant that the smaller number, M4253, is considered never to have been the largest discovered Mersenne Prime.

The BBC notes that prime numbers can be useful for encryption. Some techniques take advantage of the fact that its a simple task to multiply two prime numbers together, but much more complex and time-consuming to take the resulting number and figure out what the two prime numbers were. That said, the size of the prime numbers being found today is far larger than is required for current encryption standards.

Hunting for primes can also have some unexpected benefits. Earlier this month it emerged that an obscure and unknown bug meant that trying to process a particular prime number could cause computers running the new Intel Skylake processor to freeze.