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.

Comments

If GIMPS Can Find Such a Huge Prime

[Anonymous Coward]

Just think how big a prime PHOTOSHOPS could find!

Re:If GIMPS Can Find Such a Huge Prime

[Anubis IV]

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.

Re:Application

[kaoshin]

From TFA:

"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.

Re:Application

[semper_statisticum]

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.

Headline writer is a boob

[FatRatBastard]

Subject says it all.

Thats

[JustOK]

That's amazing! I've got the same combination on my luggage!

Re:Posted by FirehoseFavorites?

[whipslash]

FirehoseFavorites is purely user voted content. Something new we are testing. Requires zero editor input to make it to the front page, just user votes from the firehose.

Re:I'll fine one right now

[RackinFrackin]

Not a rigorous proof, but here's my favorite explanation:

for any positive integer k, the binary representation of 2^k-1 consists of k 1's. If k is even, this is an even number of 1's lined up together. Since 3 is 11 in binary, you can divide 2^k-1 by 3 and get a quotient of the form 10101..01.

e.g. 2^10 = 1111111111=11(101010101)

Re:Application

[thePsychologist]

To clarify, these types of primes aren't useful for cryptography as they are much too large and not 'typical' primes.

From a theoretical perspective they are quite interesting: they are in bijective correspondence with perfect numbers and no one knows whether there are infinitely many. For all we know, this one could theoretically be the last.

Re:Application

[burhop]

For all we know, this one could theoretically be the last.

OK people, we're done here! We found the last prime! Time to shut it down! You don't have to go home, but you can't stay here!

OK, that was a joke but we can still be clear. He was talking about the last perfect number. There is an infinite number of primes. That proof is pretty simple.

1. Assume there is a limited number of primes. Given the list of all the prime numbers
2. Multiply them all together and add 1.

The new number you get is can not divisible by any of the prime numbers in your list (e.g. if you divide the number by 2, you have a reminder of 1, if you divide the number by 3, you have a remainder of 1, if you divide the number by 5, you have a remainder of 1...)

So there must be at least one number not on your list which invalidates the given statement.