back to article GIMPS crack whip on plucky processor to find largest prime number

The Great Internet Mersenne Prime Search (GIMPS) has announced the discovery of a new largest Mersenne prime number, 277,232,917 -1. The figure, viewable here (.zip file), was found by GIMPS' network of volunteer prime hunters, and is the 50th Mersenne prime discovered. It comprises 23,249,425 digits, and is 910,807 digits …

  1. James 51
    Joke

    but has since been put to practical use in cryptography

    So, how long before the FBI asks to ban prime numbers?

    1. TechnicalBen Silver badge
      Mushroom

      Re: but has since been put to practical use in cryptography

      All numbers can be factored into primes. So the only way to be safe is [see icon]!

      1. elDog

        Re: but has since been put to practical use in cryptography

        I suggest that mere mortals are required to use a non-decimal numbering system, possibly based on irrationals that would make finding primes much more interesting.

        Or maybe requiring all CPUs to only deal with floating-point numbers (no integer calculations) which would kill the processing time and eradicate any exactitude. Of course, the powers-that-be would be allowed to do integer arithmetic.

    2. Zippy's Sausage Factory

      Re: but has since been put to practical use in cryptography

      You jest, but I suspect that at some point they might well try and pass a law to make the details of prime numbers a state secret.

      That said, sillier laws have been passed in the past, and I suspect there will be in the future.

      1. Anonymous Coward
        Anonymous Coward

        Re: but has since been put to practical use in cryptography

        See: Indiana Pi Bill

        Not passed but really stupid.

        1. The Bloke next door

          Re: but has since been put to practical use in cryptography

          No more up votes .. 3 is enough.

    3. davidp231

      Re: but has since been put to practical use in cryptography

      Never mind the Fubby (FBI)... just don't tell Amber Fudd or she will get ideas way above her station (git central).

    4. JimmyPage Silver badge
      Stop

      Re: but has since been put to practical use in cryptography

      Not a joke

      https://en.wikipedia.org/wiki/Illegal_number

  2. Hairy Spod
    Paris Hilton

    Has anyone double checked to see if it can be divided by 3?

    Whenever we had to find prime numbers at school the ones I 'found' were usually divisible by 3.

    1. Fading Silver badge

      Just add the digits together....

      If the resulting number is divisible by three then the original number was......

    2. John H Woods Silver badge

      mod 3

      Pretty easy to check --- all multiples of three, expressed in base 10, has a digit sum which is also a multiple of three (and can therefore be checked by the same rule).

      1. This post has been deleted by its author

        1. charlieboywoof

          Re: mod 3

          It goes up to eleven?

        2. labourer

          Re: mod 3

          This simplifies to 3 divides 2^n-1 if and only if n is even, so we're good, it's not divisible by three. Phew.

    3. bombastic bob Silver badge
      Devil

      "Whenever we had to find prime numbers at school the ones I 'found' were usually divisible by 3."

      yeah too much busywork, doing all of those divisions. Imagine doing it WITHOUT an electronic calculator. That would be when _I_ was in school... through Jr. High anyway.

      thinking of high school, I had a friend who came up with a really interesting way of calculating prime numbers. He proposed prime numbers "by addition", basically a set of 'for' loops that marked an array (you could use a bit array) for every value divisible by 'n' and then you just examine the array afterwards and print out anything with a zero in it. It would be significantly faster than dividing by every odd integer <= sqrt(number), but maybe not faster than dividing by "discovered prime numbers" <= sqrt(number). Anyway, for a value of this magnitude (re: article's number), I think you'd run out of RAM...

      (then again it's only 2 ^ 77 million, so perhaps not?)

      1. Vulch
        1. bombastic bob Silver badge
          Devil

          "Known as the Sieve of Eratosthenes."

          thanks, I obviously hadn't heard of that one.

  3. Aaiieeee
    Angel

    Thats my new password sorted

    I'll just add 1 letter and symbol in random places and perhaps remove a few digits from the middle and I should be good to go!

    1. rh587 Silver badge
      Joke

      Re: Thats my new password sorted

      I'll just add 1 letter and symbol in random places and perhaps remove a few digits from the middle and I should be good to go!

      Two letters surely - one uppercase and one lowercase?

      1. PNGuinn
        Headmaster

        Re: Thats my new password sorted

        And some punctuation. shirley?

        Won't someone think of the apostrophies?

        1. Muscleguy Silver badge

          Re: Thats my new password sorted

          I had to change a password as it contained an asterisk. It was created on a Mac, but my Android phone must use a different ASCII code for asterisks or something and it simply would not work on that. Which was a pain. Here was me under the impression that ASCII was set in stone and should be the same across systems.

    2. DNTP

      Re: Thats my new password sorted

      Password Strength: Weak (needs mix of capital and lowercase letters, needs more than one special symbol, *IT Team: please insert another bullshit rule here, thanks, management*)

    3. The Bloke next door

      Re: Thats my new password sorted

      My pin number is the last 4 digits of Pi .

      1. TechnicalBen Silver badge
        Thumb Up

        Re: Last 4 Digits of Pi...

        Well, IIRC some infinities are "even", and infinity can be defined as a fraction of -1/12 (note that is *minus* one).

        So finding the "last" four digits might not be impossible in some aspects of mathematical analyses. It's the infinite set between two points that is more difficult. ;)

  4. Brewster's Angle Grinder Silver badge

    Do we really need it printed out? After all it's just 0b111..111.

  5. ffRewind

    A bloody good read actually

    ** Spoiler Alert **

    My favourite part is:

    "805527898274441538637314218125980674172584395778861841820859398697454646280030912007"

    Didn't see it coming at all, genius.

    1. Anonymous Coward
      Anonymous Coward

      Re: A bloody good read actually

      It trailed off at the end to nothing. I wasn't expecting more though.

      1. David Gosnell
        Joke

        Re: A bloody good read actually

        It trailed off at the end to nothing

        That would have meant divisibility by 2, 5 and 10 at the very least.

    2. Dinkrex

      Re: A bloody good read actually

      Paid review!

    3. Phil O'Sophical Silver badge

      Re: A bloody good read actually

      I gave up after the first chapter, it was too formulaic.

  6. Anonymous Coward
    Anonymous Coward

    Actually...

    He wasn't the first to discover it - it was the Tr0tsk1 3lit3 haxors group running a meltdown trojan on his machine that did!

  7. Anonymous Coward
    Anonymous Coward

    My favourite part...

    ...is where there are ten consecutive digits the same. Open the file and search for 9999999999 you'll find its there :)

    1. Steve Aubrey

      Re: My favourite part...

      Glad he didn't bail after seeing eight 9s in a row.

      "Gladys, the prime generator's stuck again. Whack it on the side and restart it."

      1. Bob Ajob

        Re: My favourite part...

        I'd be interested to know what the actual odds are of any specific ten consecutive digit number occurring in a truly random long digit sequence like this monster prime, I would hope its around 10^10 or one in ten billion? I searched for the same string sequence (9999999999) in the decimal digits of pi and couldn't find it in the first 200 million or so, perhaps finding it so much sooner in this sequence has a very low probability?

        1. Anonymous Coward
          Anonymous Coward

          Re: My favourite part...

          100% in a truly random number - any arrangement can appear, and will, which is what confounds peusdo-random number generators hard to prove if they really are random.

          1. Anonymous Coward
            Anonymous Coward

            Infinite monkeys?

            I think the ten digit statement above is only true for infinitely long random sequences and not for a specific sequence of a given length? If the probability of finding ten recurring digits in any randomly generated number sequence are less than one in the FIRST few billion digits then the odds of a specific ten digit sequence turning up far sooner (in say tens of millions of digits rather than billions) that should be much lower but perfectly acceptable, just less than 1% maybe? Isn't this how bitcoin miners use sha256 hash collisions for proof-of-work, as the odds of finding a really large (2^256) number with lots of recurring leading zeroes is extremely low for randomly generated inputs but every now and then someone in the pool gets lucky and guesses sooner than expected? You wouldn't expect to find the complete works of Shakespeare (or even the first page of Hamlet!) to ever be generated using monkeys on typewriters during the expected age of the universe due to the probability being 1 in 26 to the power thousands of characters?

            https://en.wikipedia.org/wiki/Infinite_monkey_theorem#Probabilities

            1. Anonymous Coward
              Anonymous Coward

              Re: Infinite monkeys?

              Probabilities - wiki? load of bollocks. A truly random number has no probable outcome nor odds. Any sequence can appear in an infinite number: if it is probable then is is random? yes and no - the cat is dead or alive.

              The probability of me winning the lottery is 50% - I either win it or don't.

              1. PNGuinn
                Holmes

                Re: Infinite monkeys?

                And the probability of me winning the lottery is 0% - I only bet on selected certainties - and making Camelot rich isn't one of them.

                1. Anonymous Coward
                  Anonymous Coward

                  Re: Infinite monkeys?

                  That isn't probability - that is odds or chance.

          2. Anonymous Coward
            Anonymous Coward

            Re: My favourite part...

            Randomness isn't even, it's clumpy, like cosmic background microwave radiation. Anyone know of a really, really good random number generator?

            1. Destroy All Monsters Silver badge
              Headmaster

              Re: My favourite part...

              There is structure in primes:

              Mathematicians Discover Prime Conspiracy: A previously unnoticed property of prime numbers seems to violate a long-standing assumption about how they behave.

              Among the first billion prime numbers, for instance, a prime ending in 9 is almost 65 percent more likely to be followed by a prime ending in 1 than another prime ending in 9.

            2. Anonymous Coward
              Anonymous Coward

              Re: My favourite part...

              Anyone know of a really, really good random number generator?

              Despite frequentists' conniptions, probabilities ARE ontological and Nature has very good generators with fixed values built-in: HotBits: Genuine random numbers, generated by radioactive decay.

              1. Anonymous Coward
                Anonymous Coward

                Re: My favourite part...

                Cheers dude that's epic! I was considering getting one of those USB key things with some sort of decay based generator built in but this is more expedient.

        2. Anonymous Coward
          Anonymous Coward

          Re: My favourite part...

          (Beware line breaks every 100 characters)

          I was disappointed to find that 0118999 wasn't there - let alone the rest of it.

          For Pi fans: 3141592 is there, but not 31415926.

          There are 23,714,413 decimal digits; so an arbitrary sequence of 7 digits (of which there are 10 million combinations) has a reasonable chance of being there.

          Looking at sequences of repeated digits, the largest ones are:

          zeros - 7

          ones - 7

          twos - 8

          threes - 8

          fours - 7

          fives - 7

          sixes - 8

          sevens - 6

          eights - 7

          nines - 10

          So nine does seem to be a special case.

    2. Anonymous Coward
      Anonymous Coward

      Re: My favourite part...

      If you dialed that when being murdered, you might be lucky and get two copper's arrive fresh from the kebab shop 6 hours later.

    3. Anonymous Coward
      Anonymous Coward

      Re: My favourite part...

      If you reverse the nines is it still a prime number?

  8. This post has been deleted by its author

  9. Anonymous Coward
    Anonymous Coward

    As used by the accounting department

    http://dilbert.com/strip/2001-10-25

  10. fobobob
    Headmaster

    Pedantic Grammar Nazi Inbound, 9 o'clock!

    ... comprised of ...

    Should probably be "composed of" or "comprises".

    1. keith_w Bronze badge

      Re: Pedantic Grammar Nazi Inbound, 9 o'clock!

      So why didn't you complain about copper's, which is possessive and should have been coppers, plural or, if they had the kabobs with them coppers' (plural possessive) kabobs (plural, non-possessive)?

  11. maddddog

    FAKE NEWS

    The real 50th Mersenne prime is 2**77,232,917 -1

    1. Drewc (Written by Reg staff) Gold badge

      Re: FAKE NEWS

      Well, maddddog, that changes everything.

  12. Chris Miller

    Perfect

    We also have the world's largest known perfect number:

    277,232,916(277,232,917-1)

    It's an open question whether there exist any odd perfect numbers, but any that do exist must be greater than 101500.

  13. GrumpenKraut Silver badge
    Pint

    Appreciation pint

    ...for defining primes as "numbers only divisible by one and themselves".

    Prost!

    1. DavCrav Silver badge

      Re: Appreciation pint

      Technically, a prime is an integer p such that 1) p is not a unit (i.e., 1 or -1), and 2) whenever p divides ab, then p divides a or p divides b (or both). What is described here are irreducibles, not primes. That primes and irreducibles are the same thing is the definition of a unique factorization domain. (All primes are irreducible, but not all irreducibles are prime.)

  14. This post has been deleted by its author

  15. Not also known as SC
    Joke

    42

    So we still don't know where Deep Thought got 42 from then?

    1. The Nazz Silver badge

      Re: 42

      Fortitude?

      It may not be the answer to everything but it sure does help.

  16. DNTP

    Let me save you all some trouble

    "69" occurs 229,286 times (first instance: digit 255)

    "420" occurs 22,948 times (first instance: digit 613)

    "80085" occurs 217 times (first instance: digit 145943)

    Interesting pattern to note: The frequency of each number decreases proportionally to the length of that number, almost exactly to the rate of one order of magnitude per additional digit. It's almost like... base 10 or something.

    1. This post has been deleted by its author

  17. Mark 85 Silver badge

    Will there ever be an end to this? If so, will that number contain the number of digits that's a prime number?

    Yeah... it's after beer o'clock and the mind wanders...

  18. Spiz

    Off topic...

    ...but I do giggle to myself when I can read the intelligent, thought-inspiring comments on a Reg thread, swipe straight past anything that is headed with “bombastic bob” and see just a few milliseconds glimpse of his/hers downvotes before I read then next post.

    Happy New Beers :)

  19. David Gosnell

    5318008

    It's in there. Just the once though.

  20. Mike Shepherd
    Meh

    Yawn

    Call me when they have the first for π(x) > li(x) (estimated about 10316).

  21. Anonymous Coward
    Anonymous Coward

    Missed Opportunity

    Look, tie Mersenne Prime search to a block chain, Einsteinium for example. Payout in EMC2 when a prime is found. You'll have so much computing power, new Primes will be popping like corn.

    Although the finders likely won't be boffins, so it will deprive El Reg of its customary reporting style...

  22. Qwertius
    Trollface

    A Girl called Pi.

    I once new a girl called Pi

    She had the most infinite eyes.

    I once tried to kiss her

    but her fists moved much quicker

    so all that I got was -- black eyes.

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