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Mathematicians claim record in search for rare prime numbers

latimes.com — UCLA mathematicians appear to have won the $100,000 prize from the Electronic Frontier Foundation for discovering the first verified Mersenne prime number with more than 10 million digits.

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  • fafnir314, on 09/26/2008, -2/+33That's a pretty bit of money for finding a prime number
    • edicius, on 09/27/2008, -7/+2I'll save them a lot of trouble for next time. You don't find numbers, they come one after the other in sequence. Check please!
    • bwdd, on 09/27/2008, -0/+3Well, can you imagine how long it took them to find it?
  • edwinjose, on 09/26/2008, -13/+4Mathematicians are increasingly becoming empirical and constructivist like the programmers. Perhaps, they are starting to take Godel seriously...
    • unique172, on 09/27/2008, -0/+11Please explain what you mean? Every mathematician I know, especially number and set theorists, take Godel very seriously, since his findings are painfully obvious at the upper reaches of mathematics (as one bumps against the Axiom of Choice, etc.)

      Additionally, many number theorists are also programmers, since the only way to find such large numbers and verify their primality is to use computers.
      • edwinjose, on 09/27/2008, -0/+2What I meant was: Mathematicians of the past wanted proofs for everything. But nowadays they are more willing to accept that there are things that are very very likely to be true but might never have a proof.

        So the new mathematicians use conjectures that have been verified to be true for a large number of cases using a computer, in the hopes of hitting on other very very probable truths.

        Sorry to sound so philosophical.
      • fx666, on 09/28/2008, -0/+1"But nowadays they are more willing to accept that there are things that are very very likely to be true but might never have a proof"
        Very few mathematicians are willing to accept this concept, their number is less that 0.1% of the total number of mathematicians. Besides, your remark has nothing to do with the Godel proof of existence of unprovable logical propositions.
        For more information, consult the book On Existence of Unprovable Propositions by Godel.
  • SaumZ, on 09/26/2008, -1/+28Running that program on a computer is just like playing the lottery - someone is bound to "win" sometime.
    • eSentrik, on 09/27/2008, -0/+13Brute force algorithm + super computer + waiting FTW?
    • dokon, on 09/27/2008, -1/+3Except that there is no guarantee that there are more Mersenne primes.
      • thewhizforever, on 09/27/2008, -0/+0why? c'mon don't spoil the fun!
        lets hope there are more = more money
  • nmezib, on 09/26/2008, -29/+4congrats to the mathematicians!

    now I'm going to continue doing stuff that is actually helpful to humankind.
    • wonderchemist, on 09/27/2008, -1/+35Like posting on Digg?
    • IglooBurner, on 09/27/2008, -2/+17Mathematicians and the subject of math is probably the most beneficial gift to the development of our civilization.
    • whahaa, on 09/27/2008, -2/+37prime numbers are a vital part of cryptography, which is a vital part of national security. why do you hate freedom?
    • sc0rpi0n, on 09/27/2008, -4/+4Longer prime number = Tougher cryptography. That's why reward is $100,000.
      • NathanielJ, on 09/27/2008, -0/+6No, that's not why the reward is $100,000. Prime numbers of a few hundred digits are useful for cryptography. Prime numbers with millions of digits are absolutely useless for RSA encryption because
        1) they take too long to compute with
        2) only a handful of them are known, so someone wishing to break the cryptography would only have to check a handful of them
    • Desurivative, on 09/27/2008, -2/+21Oh, you ignorant son of a bitch.

      Just because you have some kind of "SKOOL IS 4 LOZERZ" attitude and don't understand how our society has benefited from mathematics (or in this particular case, the uses of prime numbers for cryptography, for instance) doesn't mean there is nothing useful for humanity here. Somehow I doubt whatever occupation you have for yourself as a corporate drone or sales monkey or whatever benefits society as much as you would like to think.

      Also, many fields and discoveries in mathematics have been made throughout history before practical applications had been found for them. Boolean algebra and all sorts of discrete math, for instance, were conceived before we had digital computers, in some cases with the idea "wouldn't it be neat if we had machines that could follow these sets of rules...?" But you're probably one of these people who thinks computers run on magic and only plays games.

      TL;DR ***** you.
      • mooseontheloose, on 09/27/2008, -0/+3Psst... he's trolling.
      • nmezib, on 09/27/2008, -0/+1lol thank you Moose, I was totally being a troll. :P people love getting defensive over their babies

        and for your information, Desurivative, I'm in toxicology research at the University of Pittsburgh graduate school of public health. We study levels of arsenical contaminants in drinking water around the world and in the US, with the hopes of providing treatments against chronic Arsenic exposure.

        I know prime numbers are an indispensible part of most of science. Jesus, how stupid did you REALLY think I am?
    • OrangeTide, on 09/27/2008, -0/+2Yea. Prime numbers are useless until you need some prime numbers for algorithms, particle physics, chemistry, genetics, mechanical engineering, ...
      • ljw5021, on 10/07/2008, -1/+1You're retarded. Just because easy fields don't use it means it's not useful?

        Enter cryptography.
    • hmunkey, on 09/27/2008, -1/+2Um.... math is pretty much behind every scientific, technological, and medical innovation in some shape or form. You, sir, are an idiot.
  • randomchild, on 09/27/2008, -11/+6prime numbers are not rare, there are infinitely many...
    • marca17, on 09/27/2008, -2/+1Did you read the article?
    • atb12688, on 09/27/2008, -2/+2Yeah, but you didn't do this, did you?
    • NathanielJ, on 09/27/2008, -2/+3Yes, they are rare, despite there being infinitely many of them. To see this mathematically, it can be proven that as N goes to infinity, if you pick a random number (uniformly) from the set {1, 2, ..., N}, then the probability that the number you pick is prime is 0.
      • noumuon, on 09/27/2008, -1/+4except, the prime numbers are countable. therefore the set of prime numbers is as large as the set of natural numbers and integers. therefore you can argue that the primes are as equally as common as the natural numbers.
      • NathanielJ, on 09/27/2008, -1/+2@noumuon - Yeah, I know they're both countable, I never said otherwise. However, cardinality is not the only way to compare sets of infinite size. The Cantor set on [0,1] has the same cardinality (uncountable) as the whole interval [0,1], yet it has Lebesgue measure 0, which means that if you pick a number uniformly at random from the interval [0,1], then there's a 0% chance that you will pick a number from the Cantor set, even though the sets have the same cardinality.

        This is the same thing, except with countable sets.
      • bliz, on 09/27/2008, -1/+1Yeah, it's about cardinality.
  • cxt70, on 09/27/2008, -7/+19math... ***** yea!
  • atb12688, on 09/27/2008, -8/+2Is it just me, or does the LA Times desperately want to be the NY Times? I mean, the color scheme is pretty much exactly the same...
  • chaos13037, on 09/27/2008, -13/+5They found a prime number with 10 million digits, the only known larger number is the number of people who don't care.
    • danielttt, on 09/27/2008, -3/+1Dude, you gotta know something....there aint that many people here. That tends to make your words sound stupid. Not surprisingly.
  • CosmoKramer, on 09/27/2008, -6/+2A real-life Max Cohen?
    ~Arronofsky referrence
  • metapop, on 09/27/2008, -3/+14gotta catch 'em all!
  • Typhoon2009, on 09/27/2008, -2/+8In all seriousness: what's the significance of this? Not trying to sound like a dick, I'm curious to know what advances in *whatever* could come from discovery of rare prime numbers.
    • jpmoney03, on 09/27/2008, -4/+13data encryption
      • santaliqueur, on 09/27/2008, -1/+4No, primes that large are totally useless for data encryption.
    • WalkerTXclocker, on 09/27/2008, -2/+20From wikipedia:

      "For a long time, number theory in general, and the study of prime numbers in particular, was seen as the canonical example of pure mathematics, with no applications outside of the self-interest of studying the topic. In particular, number theorists such as British mathematician G. H. Hardy prided themselves on doing work that had absolutely no military significance.[19] However, this vision was shattered in the 1970s, when it was publicly announced that prime numbers could be used as the basis for the creation of public key cryptography algorithms. Prime numbers are also used for hash tables and pseudorandom number generators.

      Some rotor machines were designed with a different number of pins on each rotor, with the number of pins on any one rotor either prime, or coprime to the number of pins on any other rotor. This helped generate the full cycle of possible rotor positions before repeating any position."

      See, it's not that hard.
    • unique172, on 09/27/2008, -0/+6The excitement of the find only makes sense in a historical context. There is not now, nor has ever been, an efficient way to produce larger prime numbers. Finding large primes and proving that they are prime (neither of which is trivial) is an active area of mathematical research, and I suspect every mathematician in this field hopes they will eventually find a way to produce primes efficiently, as well as factor large numbers.

      Ironically, progress in this field is actually detrimental to data encryption, since the security of the RSA encryption algorithm depends on our inability to factor large numbers. There are similar cash prizes for finding methods to do so, since the giver of the prize would rather pay the money and know the state of the industry than continue to use an algorithm that's been compromised.
    • digg1520, on 09/27/2008, -5/+1I'm all for science and research, but this is a waste of energy and money. The numbers are useless. They are a whole different order of magnitude than the numbers used in encryption, and there is no reason why finding prime numbers with millions of digits should in any way help understanding prime numbers. And should at some point someone find an application for prime numbers that large, computing hardware will have progressed so far that all these results that now take years to compute could be reproduced in a fraction of that time.
  • NigerianHair, on 09/27/2008, -4/+1I read an article not too long ago that claimed the world economy would collapse, but science would greatly advance if the way to factor large numbers were discovered. Is anybody here able to shed some light on this?
    • unique172, on 09/27/2008, -0/+1link?
      • NigerianHair, on 09/27/2008, -0/+0Sorry, not sure how I got to the article. I know I clicked through several times, starting with Wikipedia's prime numbers entry though.

        I remember it saying the economic turmoil would likely occur because the encyrption for e-commerce depended so much on the prime scramble method of securing data.

        And the benfits to science were in the computing field, where large data could be broken down.
    • NathanielJ, on 09/27/2008, -0/+3That's because RSA encryption is based on the fact that we believe it is "hard" to factor large numbers. If an efficient way to factor large numbers were discovered, then all internet encryption would be broken (as well as various other encrypted mediums), thus making bank website etc completely insecure. Hence the supposed economic collapse that you mentioned. The "science would greatly advance" thing I imagine is a mistake on the part of the person who said it, since it is commonly believed that number factoring is NP-complete, but that's not actually known.
      • noumuon, on 09/27/2008, -1/+1it currently is np-complete. that term is applicable to problems with no *known* algorithms for quick solubility of complex problems of the type.
      • NathanielJ, on 09/27/2008, -1/+1@noumuon - Um, no, that's not what NP-complete is at all. NP-complete refers to a problem that, if it could be solved efficiently, then ALL other NP problems could be solved efficiently as well. It's the second defining property here:

        http://en.wikipedia.org/wiki/NP-complete

        Please stop replying to me with complete and utter BS.
      • noumuon, on 09/27/2008, -1/+1"The most notable characteristic of NP-complete problems is that no fast solution to them is known; that is, the time required to solve the problem using any currently known algorithm increases very quickly as the size of the problem grows."

        work backwards from that.
      • NathanielJ, on 09/27/2008, -1/+1You can't take one sentence and completely ignore the rest. Holy GOD. That is one CHARACTERISTIC. That is, if a problem is NP-complete, then it has that property. It does NOT go the other way. Having that property does not make a problem NP-complete.

        For god's sake, the definition of NP-complete is right there at the top of the page.

        Edit: Here, maybe this will help you: http://en.wikipedia.org/wiki/Integer_factorization
        Quote: "It is suspected to be outside of all three of the complexity classes P, NP-Complete, and co-NP-Complete."

        Get it? NP is not the same as NP-complete. Also, the fact that no *known* algorithm exists has nothing to do with its computational complexity class. It is UNKNOWN where it lies in the world of computational complexity.
  • jptolife, on 09/27/2008, -9/+3Ok, time for them to get laid now.
  • diceau, on 09/27/2008, -7/+2GIMPS ... *snigger*
  • sinkingshriek, on 09/27/2008, -4/+2who would have thought that there would be a news about this someday!!???
  • opticwind, on 09/27/2008, -3/+2Didn't this happen like 3 weeks ago?
  • Tichondrius74, on 09/27/2008, -7/+2Damn you onion... oh wait this is real? How the hell?
    • santaliqueur, on 09/27/2008, -0/+2Yeah, The Onion really loves that prime number humor.
  • RedneckRandy, on 09/27/2008, -10/+2So what the ***** is the use for this?? Why spend all that money on time on something as completely useless as this!?
    • danielttt, on 09/27/2008, -2/+6There are important things in this world small minds cannot grasp. Lack of education exacerbates this. Lack of common sense, though, tends to thoroughly illuminate respondents on these related fora for their imbecilic inclinations as I'm sure you would agree.
      • xcbxcb, on 09/27/2008, -4/+6Typing unintelligible prattle doesn't make you smart or clever or high-minded or interesting.

        It makes you a *****.
      • supermanly, on 09/27/2008, -3/+1"'For a long time, number theory in general, and the study of prime numbers in particular, was seen as the canonical example of pure mathematics, with no applications outside of the self-interest of studying the topic. In particular, number theorists such as British mathematician G. H. Hardy prided themselves on doing work that had absolutely no military significance.[19] However, this vision was shattered in the 1970s, when it was publicly announced that prime numbers could be used as the basis for the creation of public key cryptography algorithms. Prime numbers are also used for hash tables and pseudorandom number generators.'"

        Some rotor machines were designed with a different number of pins on each rotor, with the number of pins on any one rotor either prime, or coprime to the number of pins on any other rotor. This helped generate the full cycle of possible rotor positions before repeating any position."

        Copied from an above post which was copied from Wikipedia.

        Nice job at making yourself look like an idiot danielttt. Your skill at answering questions MAY exceed even Sarah Palin's.
      • digg1520, on 09/27/2008, -0/+2Good luck encrypting with 10.000.000 digit long prime numbers.
      • danielttt, on 09/27/2008, -1/+3supermanly ... Glad to see you've discovered google, wikipedia and the copy/paste function on your keyboard. You might now start working on an ability to understand satirical discourse.

        xcbxcb ... I'm sorry if If your vocabulary (the words you know how to use) stops you from understanding what's I wrote above. I certainly understand why you relate to RedneckRandy. I am curious though, why would you presume me to be homosexual. Where's the connection between one's ability to write a simple sentence with multisyllabic wording and homosexuality....?

        I resent people who don't use their heads. My response is intended to illustrate the RedneckRandy's narrowminded kneejerk reply to something he doesn't understand. I am sorry he lacks the curiousity to look into things further. His public vulgarty is offensive to me and begged for a satirical response. I don't pretend to be of anything more than average intelligence.
      • RedneckRandy, on 09/30/2008, -0/+2Actually Danielttt, despite my screenname I am a thinking invidual who happens to have an engineering degree and a fine grasp of mathematics and science. I understand that mathematical constructs can have non-obvious applications and even unforeseen applications sometime in the future. However, I think this particular finding is absolutely useless. As digg1520 said, good luck encrypting with a 10million digit number. Perhaps it is you who is the small minded imbecil who judges someone simply on their name. I raised a valid question. You are the one who responded with idiotic non-sensical self-righteous egotistical drivel that did not answer my question at all.
    • disrupter, on 09/27/2008, -1/+4you live up to your name
  • jfreshbloomer, on 09/27/2008, -5/+6In other news, UCLA mathematicians are still not getting laid...
  • BruceNolan, on 09/27/2008, -2/+0Is there any upper limit on the highest prime no? Or else is there an infinity?
    • NathanielJ, on 09/27/2008, -0/+3Infinity. Check Wiki for a simple proof.
    • thewhizforever, on 09/27/2008, -0/+1this not a formal proof, but logic: if there is an infinite amount of numbers that exist, then there is an infinite amount of primes.
  • OrangeTide, on 09/27/2008, -0/+2When can we look for non-Mersenne primes?
  • xGeneric, on 09/27/2008, -0/+3Go Go Prime95!
  • goon5000, on 09/27/2008, -1/+0I found out that the number 3 is prime, where's my money?
    • EricJ2190, on 09/27/2008, -0/+1It's a Mersenne prime, too. 2^2-1.
  • The_Dude, on 09/27/2008, -1/+1so is this gonna help our PIN numbers be more secure?
    • EricJ2190, on 09/27/2008, -0/+3It will if you use that whole number as your PIN.
  • Kaystar87, on 09/27/2008, -3/+1"Mathmaticians find the first verified Mersenne prime number with more than 10 million digits."
    In other news, "Scientists are still looking for said "mojo" in Austin Power's film".
  • m4xn00b, on 09/27/2008, -0/+1prime 95 brings my rig to its knees.
  • EricJ2190, on 09/27/2008, -1/+2So I guess I can stop making my computer work on 2^44026159-1. Screw it, I am finishing this anyway.
  • kelmaster1, on 09/27/2008, -0/+2go GIMPS!
  • rootbeerinacan, on 09/27/2008, -2/+1Is THIS where my EFF donations go?
  • xcbxcb, on 09/27/2008, -2/+1*****.
  • goon5000, on 09/27/2008, -2/+0wake me up when you have an algorithm that determines prime in milliseconds and not months.
  • solid12345, on 09/27/2008, -1/+1Not as momentous as the person who discovered the number 69...
    • goon5000, on 09/27/2008, -0/+0I like to think that yo momma and I discovered it together.
  • LordoftheFly, on 09/27/2008, -2/+1But will it run Crysis?
  • floejoe, on 09/28/2008, -1/+2It was on a network of Windows XP machines too, by the way.
  •  

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