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$2^{77,232,917}-1$ is the new $2^{74,207,281}-1$

We now know 50 Mersenne primes! The latest indivisible mammoth, $2^{77,232,917}-1$, was discovered by Great Internet Mersenne Prime Search user Jonathan Pace on the 26th of December 2017. As well as being the biggest Mersenne prime ever known, it’s also the biggest prime of any sort discovered to date.

GIMPS works by distributing the job of checking candidate numbers for primality to computers running the software around the world. It took over six days of computing to prove that this number is prime, which has since been verified on four other systems.

Pace, a 51-year old Electrical Engineer from Tennessee, has been running the GIMPS software to look for primes for over 14 years, and has been rewarded with a \$3,000 prize. When a prime with over 100 million digits is found, the discoverer will earn a \$50,000 prize. That probably won’t be for quite a while: this new prime has $23{,}249{,}425$ decimal digits, just under a million more than the previous biggest prime, discovered in 2016.

If you’re really interested, the entire decimal representation of the number can be found in a 10MB ZIP file hosted at mersenne.org. Spoiler: it begins with a 4.

More information: press release at mersenne.org, home of the Great Internet Mersenne Prime Search.

via Haggis the Sheep on Twitter

New Mersenne primes not discovered

The Great Internet Mersenne Prime Search, the premier distributed-computing prime finding initiative, has reported that $M_{32582657} = 2^{32,582,657}-1$, the 44th Mersenne prime to be discovered, is also the 44th Mersenne Prime in numerical order. It was found by Steven Boone and Curtis Cooper in 2006 (Cooper also discovered the current largest prime as reported here in February), but until now it was not known for certain that other, smaller primes had not been overlooked. GIMPS has now checked all the intervening Mersenne numbers for primality and having found nothing, $M_{32582657}$ is secure in its 44th-ness.

Further information

The Great Internet Mersenne Prime Search (announcement on the front page as of November 10)

Their page for the prime itself

Mersenne Prime at Wolfram Mathworld

via @mathupdate on Twitter