Largest prime number discovered (so far)!

Discussion in 'Current Events' started by stonyc, Jan 4, 2006.

  1. neocell macrumors 65816

    neocell

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    #2
    I read this this morning and I though, 'who the f cares'. Think of all the processing power that was used and what came of it? Am I missing something here or is this find useful, besides to get these guys names posted somewhere. Why not use that computer time folding or SETI or something else with potential. If anyone can see a benefit of this find please elaborate. Thanks
     
  2. 2nyRiggz macrumors 603

    2nyRiggz

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    #3
    ^^LOL....i must say i was thinking the same thing but then again still an interesting read....if u are into that sorta thing...which im into:rolleyes:


    Bless
     
  3. mkrishnan Moderator emeritus

    mkrishnan

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    #4
    Wait, so do they believe that this is *the* largest Mersenne prime number, or just the largest one they found so far? If it was the former, it would be really interesting, if there's a proof to back it up.....
     
  4. Doctor Q Administrator

    Doctor Q

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    #5
    What a misleading headline. There are an infinite number of prime numbers, so there can be no largest one.

    The easiest type of prime to find is a Mersenne prime, a prime that is one less than a power of two. For example, 2^30402457-1 is a Mersenne prime.

    The article title should have been "Researchers discover new prime number" or "Researchers discover new largest-known prime number".

    By the way, it isn't known whether there are infinitely many Mersenne primes, so in theory they could have discovered the largest Mersenne prime!
     
  5. PlaceofDis macrumors Core

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    #6
    thanks for that info DocQ. i don't do well with numbers myself. i didn't know that there were more than one kind of Prime numbers out there. you learn something new everyday huh? :cool:
     
  6. Doctor Q Administrator

    Doctor Q

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    #7
    Here's a real mind-bender: I can describe a prime number for which I'll never know the actual digits:

    I hereby define the "Post-Doctor-Q Prime" to be the first prime number discovered after I die. We know some facts about this number, namely that it is prime, has not yet been discovered, is not the largest prime number there is, but will be the largest known prime number at the time. We even know that it's an odd number. Since the actual digits of a large prime number are of less interest than its properties, you know almost all that is interesting about the number I've described, even though nobody knows what the number actually is!

    Maybe the Post-Doctor-Q Prime would make a nice topic for some "post-doctoral research" :D by a math major. Or better yet a philosophy major.
     
  7. mkrishnan Moderator emeritus

    mkrishnan

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    #8
    Yes, I make abuse of this logic all the time! :eek: :eek: :D

    Thank you for the explanation! :)

    Is every number of the form 2^n - 1 a prime? That can't be true....

    2 4 8 16 32 64 128 256 512 1024
    1 3 7 15 31 63

    Hmmm, okay, so they're not all primes.... so it is possible that there's a largest one. But it's not certain. And I guess all these people did was keep multiplying by two and checking for a prime?
     
  8. Doctor Q Administrator

    Doctor Q

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    #9
    They ran the GIMPS software. I don't know if GIMPS currently uses the Lucas-Lehmer method to determine if a given Mersenne number is prime, but the methods are much more efficient than simply testing for all possible divisors of each number of the form 2^n-1.

    Would you like one of these for your birthday?
     
  9. clayj macrumors 604

    clayj

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    #10
    No, there really is no possibility of finding THE largest prime number. This one was just the largest one found so far.

    How they check to see if a number is prime is actually not that complicated, but it takes a LOT of computing power, especially for the larger primes. There are a few "rules" that help simplify things... for example:

    1. For the sorts of numbers they're checking (i.e., BIG numbers), no prime number will end in 2, 4, 5, 6, 8, or 0. Only numbers that end in 1, 3, 7, and 9 need to be checked to see if they are prime. (Any number that ends in 2, 4, 6, 8, or 0 is obviously divisible by 2; any number that ends in 5 is obviously divisible by 5. So only ...1, ...3, ...7, and ...9 can be prime.)

    2. If the sum of the digits of a number is divisible by 3, then the number is ALSO divisible by 3 and hence NOT prime.

    3. For any number "n", the LARGEST factor that you actually have to check for even divisibility is the integer portion of the square root of "n". For example, if you want to check for primes for 991, the square root of 991 is 31.4801524... so, if there are ANY factors for 991, one of them will be less than or equal to 31.

    So, for this new number, 2^30402457, the largest factor you'd have to check is around 2^5514, which is ROUGHLY the square root of 2^30402457. 2^5514 is still a huge number; it's 7.575235e1659, or a number with roughly 1660 digits. (Here's how absurdly LARGE that number is; one estimate of the number of atoms in the ENTIRE UNIVERSE is 1e84, or a number with 84 digits.)

    Fortunately, there are other mathematical techniques (of which I have little knowledge beyond their existence) which can be used to reduce the number of potential factors. Even with all of that narrowing, though, it still takes a LOT of brute force computation to check to see if a number that large is prime.

    So, this is actually quite an accomplishment.
     
  10. PlaceofDis macrumors Core

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    #11
    indeed. given my lack of knowledge in this area i am learning quite a bit today through this thread. yay for learning. yes i am a dork. i'm posting on an online forum afterall arn't i?

    in theory though, there is no limit to how large a Prime number can be though correct? numbers run into infinity. so there is in a technical sense no way of ever finding "The Largest" because there can always be something above that.
     
  11. neocell macrumors 65816

    neocell

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    #12
    No arguing that, numbers and math are fascinating and all (good way to determine how much wine is in a barrel) but what does finding this large prime do for us? Will this help prove theories of significance or anything remotely beneficial to society?
     
  12. Veldek macrumors 68000

    Veldek

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    #13
    Prime numbers play a huge role in cryptography, for example. So if you don't want someone to hack your bank account, you better celebrate this achievement... ;)
     
  13. clayj macrumors 604

    clayj

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    #14
    As Veldek said, large primes are useful in cryptography.

    Beyond that, though, they don't have a whole lot of other use I'm aware of.
     
  14. neocell macrumors 65816

    neocell

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    #15
    Thanks for that Veldek and clayj, now I don't think it's a complete waste. Cheers
     
  15. floyde macrumors 6502a

    floyde

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    #16
    I don't think we have the hardware required to encrypt with 1Million-Bit keys yet:p At least not in a reasonable amount of time
     
  16. grapes911 Moderator emeritus

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    #17
    No, but with Quantum computers 10, 20, 30 years away we will need them.
     
  17. keysersoze macrumors 68000

    keysersoze

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    #18
  18. mcarnes macrumors 68000

    mcarnes

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    #19
    Oh baby, prime numbers give me such a hard on.
     
  19. TheMonarch macrumors 65816

    TheMonarch

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    #20
    I'm pretty sure that by then, we'd already discovered an even bigger number that even those computer would have trouble with...
     
  20. CanadaRAM macrumors G5

    CanadaRAM

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    #21
    I'll use the patented Dr. Q. prime for my cryptography -- that way nobody will know what I'm talking about until after Dr Q. passes.

    Wait, nobody knows what I'm talking about now...

    Nevermind.
     
  21. grapes911 Moderator emeritus

    grapes911

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    #22
    Definitely. Computers play a big role in finding primes. It is a very difficult process. So far, as we get faster computers that break algorithms, we find bigger primes at roughly (very roughly I might add) same rate. It works pretty well. Most people assume this will hold true even with Quantum computers. The problem will be when the government, universities, and large businesses have quantum computers and everyone else still has standard PCs.
     
  22. EricNau Moderator emeritus

    EricNau

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    #23
    I find SETI@Home to be about as useful (if not less useful) as finding Prime numbers... Who really cares?
    All those people participating in SETI@Home should consider switching to Folding@Home for Stanford University. It may help find cures for diseases such as Parkinson's, Alzheimer's, Cystic Fibrosis, and Cancer. It could save your life.
     
  23. Lacero macrumors 604

    Lacero

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    #24
    The only prime I like is juicy in the middle.


    Here's to the Crazy Ones [​IMG]
     
  24. bousozoku Moderator emeritus

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    #25
    Sure, but by the time they use it so I can log into my bank account, I'll be old and gray. My machine won't have the power to decode anything using it. How many years did it take them to find this one? I suppose using the fingers and toes method would have taken longer and they would have to hire more scientists to do it.

    Maybe now, they could use the machine to divine the winning lottery numbers so they can take a holiday away from the numbers.
     

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