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Largest Prime Number Discovered – With More Than 23m Digits (mersenne.org)
chalsall writes: Persistence pays off. Jonathan Pace, a GIMPS volunteer for over 14 years, discovered the 50th known Mersenne prime, 2^77,232,917 -- 1 on December 26, 2017. The prime number is calculated by multiplying together 77,232,917 twos, and then subtracting one. It weighs in at 23,249,425 digits, becoming the largest prime number known to mankind. It bests the previous record prime, also discovered by GIMPS, by 910,807 digits. You can read a little more in the press release.
"At present there are few practical uses for this new large prime, prompting some to ask "why search for these large primes"? Those same doubts existed a few decades ago until important cryptography algorithms were developed based on prime numbers. For seven more good reasons to search for large prime numbers, see here.
The more prime numbers that are discovered, the more likely we are to be able to discover a pattern within an arbitrary base number set. The larger numbers are useful because we also want to make sure that the entire range is consistent, or in other words that any pattern, or lack of pattern, is the same across the entire set of numbers. There is always a benefit to trying to find patterns in number theory -- it's one of the coolest and most interesting fields in pure mathematics.
The Spanish Inquisition of Psychometrics; Burning all the heretics.
Primarily for the fun of it. There are some specific uses of large Mersenne primes in the Mersenne twister algorithm for generating pseudorandom numbers https://en.wikipedia.org/wiki/Mersenne_Twister, but in practice much, much smaller Mersenne primes are perfectly fine for that use, and indeed are much more practical. There are people who whenever you talk about large primes will claim they are useful for crypto, but that's not generally the case. The primes are too big for practical Diffie-Hellman (and there are specific reasons one might want to avoid using them for that), and they are not random primes in any sense so using them for any form of RSA would be really silly. That said, there's at least one mildly fun cryptographic algorithm whose proof of correctness relies on there being infinitely many Mersenne primes http://www.di.ens.fr/~vergnaud/algo0910/Locally.pdf, but no one has to my knowledge actually tried to implement the algorithm in that paper.
Serious reply in response to a decent joke: GIMPS is the Great Internet Mersenne Prime Search, which is more or less like SETI@home or Folding@home, but for Mersenne primes. I wasn't aware what it was, so I figured I'd share. Also, I had forgotten that Prime95, which is oftentimes used to stress cooling solutions in PCs, was actually created for use in finding large prime numbers, and was apparently developed by GIMPS.
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