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Math Intel Supercomputing

New Mersenne Prime Discovered, Largest Known Prime Number: 2^74,207,281 - 1 (mersenne.org) 132

Dave Knott writes: The Great Internet Mersenne Prime Search (GIMPS) has discovered a new largest known prime number, 2^74,207,281-1, having 22,338,618 digits. The same GIMPS software recently uncovered a flaw in Intel's latest Skylake CPUs, and its global network of CPUs peaking at 450 trillion calculations per second remains the longest continuously-running "grassroots supercomputing" project in Internet history. The prime is almost 5 million digits larger than the previous record prime number, in a special class of extremely rare prime numbers known as Mersenne primes. It is only the 49th known Mersenne prime ever discovered, each increasingly difficult to find.
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New Mersenne Prime Discovered, Largest Known Prime Number: 2^74,207,281 - 1

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  • by darkain ( 749283 ) on Tuesday January 19, 2016 @11:05PM (#51333899) Homepage

    Are these people mining PrimeCoins? What's the motivation to be part of this network? Just curious is all.

    • by Anonymous Coward

      Don't ask why people are doing math, even they don't know.

      • I wanna be a perfect number! 2^74,207,281 - 1, you're so fucking special. Hahaha! That ol' monk got more credit than he deserved didn't he?
      • We've been running things like this for a couple of decades, just as SETI@Home searches for little green men, etc. I ran the GIMPS Mersenne prime search software for a couple of years on my work laptop, but it really chewed through battery life, and eventually the desktop CPUs (and GPUs, once those were supported) became enough faster that it wasn't worth contributing.

    • by dasunt ( 249686 ) on Tuesday January 19, 2016 @11:12PM (#51333929)
      You were the first comment, and you didn't take the opportunity to say "prime post!" :p
      • by Livius ( 318358 ) on Tuesday January 19, 2016 @11:53PM (#51334019)

        Obviously prime posts start with the second one.

        • by agm ( 467017 )

          Only if you fall for the dubious exception to the definition of "prime" that excludes 1 because it makes maths more convenient. :-)

          • There is nothing dubious about it. Primes are defined this way because of the Fundamental Theorem of Arithmetic. If primes were defined to include 1, there would be no such thing as a unique factorization into primes, and if that did not exist, there would be no point to the concept of primes at all.

            More generally, one of the principles of abstract algebra is that units (elements with a multiplicative inverse) can never be primes in any unique factorization domain (i.e., any ring that follows the Fundamen

            • by agm ( 467017 )

              Ok, you win. :-)

            • There is nothing dubious about it. Primes are defined this way because of the Fundamental Theorem of Arithmetic.

              While, I completely agree with you, lighten up a bit. Also, realize that in the real world the word "prime" comes from Latin primus, meaning first... hence prime steak, prime meridian, Optimus Prime, etc. And thus while in the mathy definition you're right, the real-world definition allows significant wordplay in this specific thread -- the first post is by definition a prime post, but in another sense (your sense), it's not.

        • Re:PrimeCoins (Score:5, Informative)

          by DesertNomad ( 885798 ) on Wednesday January 20, 2016 @12:11AM (#51334055)
          this is likely true as the number 1 is not a prime number. https://primes.utm.edu/notes/f... [utm.edu]
    • by Anonymous Coward

      Once you have enough for food, shelter and healthcare, only the most boring people do things for money.

    • by Anonymous Coward

      Why do anything? Nothing really matters if you stand back far enough.

      If we're going to nitpick what others do though, I think they should concentrate their efforts on finding a formula instead of brute forcing new numbers.

    • by Anonymous Coward

      What's the motivation? Apart from basic human curiosity and wanting to be part of something bigger than yourself, however pointless?

      Not much.

      But however pointless this may seem they still have a) discoverd a new prime number and b) uncovered bugs in hardware, so it's not a complete waste of time.

    • 1: to help, kind of like SETI / FOLDING@Home / et al.

      2: finding a large prime that hasn't been found yet pays ~$5k

      3: finding million digit+ primes can pay out up to ~$50K when verified.

      4: they have an old PC just hanging around and feel like helping out the math fields.

    • by armanox ( 826486 )

      No coins. Just bragging rights.

    • Prime numbers are very useful for puesdo random number generators, In this case the merssene twister. The is a huge benefit in making good rng from prime, because it can be made with an incredible simply algorithm that can run fast etc.
      • by slew ( 2918 )

        Prime numbers are very useful for puesdo random number generators, In this case the merssene twister.

        The is a huge benefit in making good rng from prime, because it can be made with an incredible simply algorithm that can run fast etc.

        Kinda, but not really. The real requirement for making a good generalized linear congruent pseudo-random number generator with a long period is to find a large galois field matrix that has a *primitive* characteristic polynomial. As it turns out it is easier to *test* if a trinomial (polynomial with 3 non-zero terms) is primitive if it is generated from a parameter related to a Merssene prime number decomposition (2^k-1). This does not guarantee that any of the trinomials generated by this parameter is prim

    • Haven't you ever been curious about something? The urge to explore? The desire to contribute to expanding the knowledge of humanity? The desire to contribute to developing useful knowledge for an important field like mathematics? The possibility of arriving at that important result yourself? The possibility of doing something useful?

      Not everyone shares those interests, especially for something as abstract as math in general, and searching for a particular form of prime number in particular.. There are

  • Mental note (Score:5, Funny)

    by aaarrrgggh ( 9205 ) on Tuesday January 19, 2016 @11:22PM (#51333945)

    Thanks, now I need to change private key.

  • by Anonymous Coward

    How the fuck do we know that? Maybe after the next one they get super easy, we have no fucking idea lol.

  • >In a special class of extremely rare prime numbers known as Mersenne primes.

    I understood that Mersenne primes are not rare, they are common compared to primes that don't fit the 2^n -1 form. Hence searching for Mersenne primes is a more efficient way of finding big ones.

  • by Anonymous Coward

    It's not new. Chuck Norris discovered in with this pocket calculator which measuring the circumference of his biceps.

  • It's small. (Score:5, Funny)

    by Kwyj1b0 ( 2757125 ) on Wednesday January 20, 2016 @01:05AM (#51334123)
    It's still smaller than the box Amazon Prime uses to send me a toothpick.
  • In1> PrimeQ[2^74207281-1]

    Now we wait.

    • by Anonymous Coward

      Heh, i would expect they make a hardcoded list for them.

  • 22,338,618 digits (Score:5, Interesting)

    by mejustme ( 900516 ) on Wednesday January 20, 2016 @01:21AM (#51334149)

    How "big" is 22,338,618 digits? Text file containing the prime is 22.8 MiB in size. http://www.mersenne.org/primes... [mersenne.org]

    • by Craig Macomber ( 3864291 ) on Wednesday January 20, 2016 @01:38AM (#51334185)

      The number is 2^74,207,281-1, thus its exactly 74,207,280 bits long and all those bits are 1. That's 9,275,910 bytes, or roughly 9MiB. When talking about mersenne primes on a tech site, using base 10 versions encoded as ascii (or utf-8, its the same for that subset) seems like an odd measure of size.

      • I was looking for a text file showing the number since obviously this prime wont fit in a uint32_t. 74,207,280 bits means nothing to me due to the size. Seeing a 22.8 MiB text file filled with digits gave it some scale.

    • But only 11 mb in packed decimal, which will be more or less as efficient when you write the number to the terminal.
  • Isn't knowing the definition of a prime number enough?
    • Re:OMG, who cares! (Score:4, Informative)

      by jandersen ( 462034 ) on Wednesday January 20, 2016 @05:40AM (#51334629)

      Isn't knowing the definition of a prime number enough?

      Enough - for what? The definition of prime numbers is deceptively simple, but we still don't know a general way to construct all prime numbers - we don't even know if there is one. The same can be said for many other classes of numbers, I suppose, but prime numbers have turned out to be useful for our understanding of numbers and other things.

      Compare with vector spces: a vector space is, to put it simply, a space with 'dimension': every point in a vector space can be represented as a tuple of numbers: a = (a1, a2, a3, ...., aN). The first thing you want to find in a vector space is the basis: a set of N vectors that point out the independent coordinate axes of the space think of R^2 or R^3, the 2- and 3-dimensional spaces we are familiar with. Every natural number has a slightly similar property: it can be written as a product of prime numbers - the prime factors. This can useful when you calculate things - if you know that 30030 = 2*3*5*7*11*13 and 136367 = 7*7*11*11*23, then it is easy to see that 136367/30030 = 2*3*5*13/7*11*23; sometimes it is easy to find prime factors, at least if you know what the prime numbers are.

      Also, in the theory for finite groups, if p is a prime number, then any group with p elements is cyclic and any group with p^2 is Abelian (wikipedia is your friend, if you want to know more); cryptic, I know, but it has profound consequences.

      • The Sieve of Eratosthenes is a general method to find all prime numbers. To the best of my knowledge, there is no algebraic function that given an integer input always produces a prime.
    • Isn't knowing the definition of a prime number enough?

      Totally. It's not like prime numbers can be applied to anything useful like cryptography.

  • So what is the big deal? I mean how will this actually change anything?

    • by Anonymous Coward

      They want to determine the bucket count for the hash map of the cosmic simulator.

  • by 140Mandak262Jamuna ( 970587 ) on Wednesday January 20, 2016 @08:15AM (#51335009) Journal
    The number of subatomic particles in the known universe is estimated to be less than 1.0e99. So if tag each subatomic particle with an integer you would run out of subatomic particles before you reach even one googol.
  • Great, now i have to change my luggage lock combination.

He keeps differentiating, flying off on a tangent.

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