Largest prime number yet discovered


From Science News:

Its size is mind-boggling. With nearly 13 million digits, it makes the number of atoms in the known universe seem negligible, a mere 80 digits. And its form is tidy and lovely: 2n-1.But its true beauty is far grander: It is a prime number. Indeed, it is the largest prime number ever found.

The Great Internet Mersenne Prime Search, or GIMPS, a computing project that uses volunteers’ computers to hunt for primes, found the prime and just confirmed the discovery

There's not a hope of printing it here: the resulting number would be 30 miles long! I figure you could stash it as 13MB or so of plaintext.

Largest known prime number found [Science News]
Distributed computing finds largest prime yet [ZDnet]

Published by Rob Beschizza

Follow Rob @beschizza on Twitter.

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  1. horay for gimps! I myself have officially tested the primality of 4 numbers and con confidently say that none of them were prime. I wonder what i will be using this massive word file for in the near future…

  2. “There’s not a hope of printing it here: the resulting number would be 30 miles long!”

    …At what font size, line spacing, kerning and paper width?

  3. This result won’t be official until we double-check it by dividing it by every prime number up to half its value. Obviously we can skip 2 by examination.

    I volunteer to do 3. Let’s see. 3 goes into 3 once, remainder zero, drop down the 1, goes into 1 zero times, drop down the 6, goes into 16 five times, remainder 1, drop down the 4, goes into 14 four times, remainder two…

    …I’ll get back to you when I’m done. Meanwhile, next person get busy on 5, after that 7, and so forth.

  4. Use a carrot Rob!!! ^!

    A carrot and what, a stick?

    Ahh, but don’t “beet” yourself up about this, Dean, these mistakes “turnip” a lot. I just wanted to “squash” this grammatical mistake right now, for my own “peas” of mind.

    “Lettuce” remember that the correct term here is “caret,” and not “carrot.” 😉

    (Sorry, I didn’t have enough “thyme” to work out the homonym/”hominy” joke…)

  5. #13: “10” in that base is not prime. I think you meant “1”. “10” would be (2^43,112,609 – 1)^2.

    In fact, in any base, anything ending in 0 is not prime.

    It’s written nicely in base 2:

    11111111…{lots of 1s omitted}…1111111

  6. Ooops.

    #13- Duh, nevermind.


    “10” is of course correct; I read it as “100”. And aything ending in “00” is not prime.

  7. #10 – you don’t need to go up to half the number, just up to its square root (as any prime factor greater then that must be a co-factor with a number less than that), so I’ve just saved you a lot of work!

  8. Great. Just great.

    Everybody’s worried about the absurd possibility of the Large Hadron Collider creating a black hole while completely ignoring the very real danger of someone reciting the 2^n-1 prime and opening the Portal of Blood.

    Well, if I manage to find the Cinnabar Diamond in time, I hope the EFF will at least be gracious enough to cover my expenses.

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