back to article 41-million-digit prime crunched by datacenter GPUs

A former Nvidia engineer has found the largest known prime number – a whopping 41 million digits long – using an A100 GPU made by his previous workplace to do the grunt work. This wasn't the CPU-heavy hunt for primes that we've typically seen. No, this time GPUs, ones more widely used for the datacenter, did all of the heavy …

  1. Eclectic Man Silver badge
    Pint

    Well done!

    And I thought I was doing ok processing 20,000 digit numbers on my old-ish Mac. Hats off to the boffin, and have one of these on me --->

    1. gnasher729 Silver badge

      Re: Well done!

      Mersenne primes have a special form. There are primality tests that work well if you have the complete factorisation of n + 1. And for Mersenne primes, we know the complete factorisation of n + 1, because (2^k-1) + 1 is just a power of two. Proving that a general number is a prime is much much much harder.

      1. Benegesserict Cumbersomberbatch Silver badge

        Re: Well done!

        for those who fancy, the folks at the Great Internet Mersenne Prime Search (GIMPS) have a ZIP archive containing all 41,024,320 digits.

        I hear the ZIP archive containing the base 2 representation is a bit smaller.

  2. Anonymous Coward
    Anonymous Coward

    Is this any more useful than "AI", or more amusing cat videos?

    An honest but likely unpopular question.

    1. RM Myers
      Happy

      Re: Is this any more useful than "AI", or more amusing cat videos?

      I doubt anyone searching for Mersenne primes does it because they think it will be useful. This has more to do with proving you can meet the challenge, and bragging rights. Much pure maths has been created with little to no expectation of usefulness, although a surprising amount has subsequently turned out to have serious importance, once the physicists, cryptologists et.al. got involved.

      1. Eclectic Man Silver badge
        Happy

        Re: Is this any more useful than "AI", or more amusing cat videos?

        Much pure maths has been created with little to no expectation of usefulness

        As a PhD pure mathematician, I'd say a great deal, probably most pure maths was created / discovered* with little to no expectation of usefulness. G H Hardy, I believe, claimed that what he had done was of no practical use whatsoever (little did he know that less than a century later, it would actually prove useful). My own thesis was on countable infinite ordinals, and useful only to other people studying them. But, the discipline of a rigorous approach, and proving things completely are useful transferrable skills, and you cannot do particle physics without learning some proper group theory, so algebra is useful too.

        *There is philosophical discussion about whether mathematics is 'created' or 'discovered. I intend to avoid this as it is beyond my knowledge and skills, although I will say, that whichever is the case, mathematical notation is created, as are the rules for manipulation. Feel free to comment on your personal perspective or not, as the case maybe.

        1. Tessier-Ashpool

          Re: Is this any more useful than "AI", or more amusing cat videos?

          The minute that ET visits Earth with a repeat proof of Fermat’s last theorem will surely be the day that mathematicians must concede discovery rather than creation.

    2. Catkin Silver badge

      Re: Is this any more useful than "AI", or more amusing cat videos?

      Should the measure of whether we permit someone to do something with resources they've paid for be whether it's "useful" or not?

    3. Catkin Silver badge

      Re: Is this any more useful than "AI", or more amusing cat videos?

      *sorry if I've misunderstood and this is more a question about possible impacts on the world at large

    4. Jason Bloomberg Silver badge
      Joke

      Re: Is this any more useful than "AI", or more amusing cat videos?

      I asked my AI and it chucked out a 2 trillion digit prime in under 5 seconds.

      AI is better and faster than everything!

      1. Michael Hoffmann Silver badge
        Trollface

        Re: Is this any more useful than "AI", or more amusing cat videos?

        Based on some of my experiences with the truthiness of "AI", I wouldn't be surprised if it spit out a number ending with "2".

        1. mostly average
          Headmaster

          Re: Is this any more useful than "AI", or more amusing cat videos?

          I mean, it would be correct if it spat out the number 2. Icon because I'm an intellectual.

        2. Beeblebrox
          Headmaster

          Re: Is this any more useful than "AI", or more amusing cat videos?

          > Based on some of my experiences with the truthiness of "AI", I wouldn't be surprised if it spit out a number ending with "2".

          There's only one 2 trlilion digit number ending with 2. All but the last digit are zero. Bravo AI.

      2. LybsterRoy Silver badge

        Re: Is this any more useful than "AI", or more amusing cat videos?

        I asked my AI to find a bigger prime number, but I told it to just print it out - just need to nip out and buy a few tonnes of paper and a few toner cartridges.

      3. Anonymous Coward
        Anonymous Coward

        Re: Is this any more useful than "AI", or more amusing cat videos?

        Taking the bait so I can ask the 'Obvious' question(s):

        Prove it !!! [Any 2 out of the following 2 will do !!!]

        a) Prove your 2 trillion digit prime is a 'prime' !!!

        b) Prove AI is 'Better' & 'Faster' than everything !!!

        P.S. Yes ... I did ignore the 'Whooshing' sound !!!

        :)

  3. nautica Silver badge
    Happy

    "The whole thing that makes a mathematician’s life worthwhile is that he gets the grudging admiration of three or four colleagues."

    --Donald Knuth

    1. David 132 Silver badge
      Thumb Up

      A relevant SMBC!

    2. Eclectic Man Silver badge
      Happy

      Or:

      "Richard P. Feynman’s speech at the Nobel Banquet in Stockholm, December 10, 1965

      Your Majesty, Your Royal Highnesses, Ladies and Gentlemen.

      The work I have done has, already, been adequately rewarded and recognized.

      Imagination reaches out repeatedly trying to achieve some higher level of understanding, until suddenly I find myself momentarily alone before one new corner of nature’s pattern of beauty and true majesty revealed. That was my reward.

      Then, having fashioned tools to make access easier to the new level, I see these tools used by other men straining their imaginations against further mysteries beyond. There, are my votes of recognition.

      ..."

      https://www.nobelprize.org/prizes/physics/1965/feynman/speech/#:~:text=I%20saw%20in%20each%2C%20joy,to%20learn%20about%2C%20their%20feelings.

      1. Antron Argaiv Silver badge
        Thumb Up

        He certainly had a way with words, in addition to being a pretty good scientist.

  4. EvaQ
    Flame

    GPU rental ... 2 million dollar

    ... Luke paid 2 million USD renting GPU's in the cloud to find this prime ...

    1. volsano

      Re: GPU rental ... 2 million dollar

      Probably still a cheaper hobby than owning a yacht.

      1. David 132 Silver badge
        Happy

        Re: GPU rental ... 2 million dollar

        Most hobbies are.

        A yacht is defined as “a hole in the water you throw money into”; Boat is a term that means “Break Out Another Thousand”.

        Still fun, though.

        1. Michael Hoffmann Silver badge
          Joke

          Re: GPU rental ... 2 million dollar

          As my wife likes to say (who was liaised with a boat fanatic many many years ago) "if you want to know what owning a yacht is like, sit in a bathtub full of water and set 100 dollar bills on fire"

          1. Sorry that handle is already taken. Silver badge

            Re: GPU rental ... 2 million dollar

            I've heard "burning* 100 notes under a cold shower"

            * although "shredding" might make more sense

    2. DS999 Silver badge

      Re: GPU rental ... 2 million dollar

      I guess he must have had a lot of Nvidia stock he kept through the big runup the last few years, so he had money to (literally) burn.

    3. Anonymous Coward
      Anonymous Coward

      Re: GPU rental ... 2 million dollar

      This doesn't surprise me at all.

      With domestic and business energy prices at a very high level, renting a server with plenty of GPU "grunt" can be quite a benefit if someone wants to make a computing-focussed donation to a project, such as GIMPS.

      And there are many hobbyists who still contribute CPU and/or GPU cycles to various BOINC projects, such as GPUGrid, PrimeGrid, etc either via their small farm of computer hosts, or by buying computing time on various cloud services, such as AWS and others.

      https://www.boincstats.com/stats/projectStatsInfo

  5. Natalie Gritpants Jr

    If you really want to see the full version of M136279841

    In binary, it is 136279841 ones.

  6. FrogsAndChips Silver badge
    Boffin

    a special class of prime numbers that are especially large

    Mersenne primes are not especially large. M2 is 3.

    1. Paul Kinsler

      Re: Mersenne primes are not especially large. M2 is 3.

      But if the number of Mersenne primes is unbounded, then presumably for any fixed choice of "large", there will be more "large" Mersenne primes than small ones, and, further, infinitely more large than non-large. Which might make it at least more-or-less reasonable to say that Mersenne primes "are large". :-)

      But perhaps what was meant that if considering all discovered "large" primes, you will notice that more of them are Mersenne than of any other type? (or some similar statement).

  7. nautica Silver badge
    Happy

    Sometimes, Mathematics may depend on one's point of view/training/interpretation (perhaps)...

    Mathematician:

    "3 is prime; 5 is prime; 7 is prime...By induction it is clear that all odd numbers are prime."

    Applied physicist:

    "3 is prime; 5 is prime; 7 is prime; 9 is pr...oops; experimental error...11 is prime; 13 is prime... Obviously, all odd numbers are prime."

    Engineer:

    "1 is prime; 3 is prime; 5 is prime; 7 is prime; 9 is prime; 11 is prime; 13 is prime; 15 is prime; 17 is pri..."

    1. talk_is_cheap

      Re: Sometimes, Mathematics may depend on one's point of view/training/interpretation (perhaps)...

      And it is clear that none of them understand the task at hand as they all missed out 2 :)

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