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GIMPS Project Discovers Largest Known Prime Number
- masterdev8 9y agoIs there a web service where you can buy a large number with certain length? Not a Mersenne prime, but just a number and/or a prime? It needs to comply with the 2^n-1 formula. Let's say I want a number long 100 000 000 or even 1 000 000 000 long. Or a prime above that length. Do you know how much would that cost per number prime and non-prime?
- MPSimmons 9y agoI believe the classic joke goes, "Now Bruce Schneier needs to change the code on his luggage"
- jcoffland 9y agotl;dr The 50th Mersenne prime was just found by a volunteer of the GIMPS (Great Internet Mersenne Prime Search) project. It is 2^77,232,917-1 and has 23,249,425 digits. Mersenne primes are extremely rare and are always of the form 2^p-1 for some positive integer p. The first four Mersenne primes are 3, 7, 31, and 127.
- meta_AU 9y agoAlso, p is prime.
- dansunciel 9y agoJust to clarify, in this case p = 77,232,917 is prime, but for Mersenne primes in general p is just a positive integer.
- meta_AU 9y agoNot quite. If p isn't prime then 2^p - 1 isn't prime.
- votepaunchy 9y agoJanuary looks to be a good month for discovering large prime numbers! As a former contributor to the project it would be great to have a primer on the best way to contribute today, covering the options for CPUs vs GPUs and the various projects for factorizations vs primality tests.
- ambivalents 9y agoAs someone who knows nothing about advanced mathematics, could someone explain why this matters? (i.e. beyond that this is rare and theoretically interesting)
- cortesoft 9y agoThe link has another link to a page describing why this matters: http://primes.utm.edu/notes/faq/why.html http://primes.utm.edu/notes/faq/why.html
- biot 9y ago> Mersennes are beautiful and have some surprising applications. Unfortunately that page doesn’t elaborate on what these surprising applications are, which is itself surprising on a page that purports to answer “why”.
- schoen 9y agoIt automatically results in the discovery of a new perfect number. :-) https://en.wikipedia.org/wiki/Euclid%E2%80%93Euler_theorem https://en.wikipedia.org/wiki/Euclid%E2%80%93Euler_theorem (combining two of history's greatest mathematicians with names that have confused generations of students by being pronounced very differently)
- Cyph0n 9y agoEuler and Gauss are (for now, at least) in my opinion the greatest mathematicians of the past two millenia (1000-1999, 2000-). Al-Khawarizmi takes the cake for the millennium before that. Then it's Euclid all the way back ;)
- jacobolus 9y agoWe know almost nothing about Euclid: we can figure out when he was active to within a century or two, and according to Pappus writing 500 years later some of his students/followers lived in Alexandria where Apollonius studied with them. That’s pretty much it for biographical details. The earliest remaining editions of the Elements have no author mentioned, and our source that Euclid compiled it is a brief remark from Proclus 700 years later. Most of what is in the Elements was results from earlier, and it’s all but impossible to break down which bits were first done when or by whom. Most of what we can see today of the Elements or Euclid’s other books is later copies, much of it probably added/changed/reordered/... later. If you want a 2000-year-old idol, go for Archimedes. In the last 1000 years, the most influential mathematician is surely Newton, with an honorable mention for Leibniz. For the computer age (from 1950 through the upcoming few centuries), I’d put my vote on Grassmann (1809–1877), though his work was long ahead of its time and still substantially underappreciated. Euler and Gauss were of course both brilliant and prolific and well worth studying, along with Descartes, Lagrange, Riemann, Poincaré, ....
- imhelpingu 9y agoSo that's what it's working on when it's starting up.
- laveur 9y agoI also was thinking of GNU Image Manipulation Project
- rootlocus 9y agoGIMPS[tartup]
- Scooty 9y ago"Loading data files" is code for "secretly computing prime numbers"
- organsnyder 9y agoGIMPS = Great Internet Mersenne Prime Search. Completely unrelated (apart from similar naming) to the GIMP (GNU Image Editing Program). Perhaps you were joking; but I'm sure others might be confused.
- Florin_Andrei 9y agoThat was very clearly a joke. Good one too.
- lettergram 9y agoI know typically jokes like this aren't HN material, but have an up vote lol Literally, the first thing I though of was GIMP as well :)
- aphextron 9y agoAgreed it's too good
- vikascoder 9y ago
- cjbprime 9y ago> Jonathan Pace is a 51-year old Electrical Engineer living in Germantown, Tennessee. Perseverance has finally paid off for Jon - he has been hunting for big primes with GIMPS for over 14 years. What a great story.
- ng-user 9y agoI know he's a volunteer but only $3000? Does that seem low to anyone else?
- bmm6o 9y agoFor producing something of no intrinsic monetary value?
- nikanj 9y agoHow are these any different from say Bitcoin?
- mlevental 9y agopeople pay for Bitcoin
- squeaky-clean 9y agoBitcoin doesn't pay out cash when you find a block. It pays out Bitcoins. So the value of that is based on how much other people will pay for a bitcoin.
- cc81 9y agoYou can buy things with Bitcoin.
- skykooler 9y agoYou can buy things with $3000 cash as well.
- mwilliaams 9y agoIs there actually any use to discovering ever-larger prime numbers?
- kss238 9y agoCryptography
- B-Con 9y agoThere's no cryptographic use in finding a largest prime. It's far larger than any prime used in a practical system and doesn't contribute any mathematical knowledge about primes. It's mostly just running an algorithm for long enough to pay off.
- madez 9y agoCome on, stop spreading nonsense. These huge primes are irrelevant for cryptography.
- sanderjd 9y agoBecause they're there...
- zeep 9y agoI know that's probably not what you mean but there is money prizes: https://www.eff.org/awards/coop https://www.eff.org/awards/coop
- netcraft 9y agoso I didn't know this, but got curious about how many known prime there are - I knew there were infinite primes, but thought that there would be some concrete list of all the primes that we had discovered somewhere - but apparently not https://math.stackexchange.com/questions/272791/how-many-prime-numbers-are-known https://math.stackexchange.com/questions/272791/how-many-pri... > Nobody's really keeping count. ... There are very many hundred-digit primes to find. We could cover the Earth in harddisks full of distinct hundred-digit primes to a height of hundreds of meters, without even making a dent in the supply of hundred-digit primes.
- TheRealPomax 9y agoThat list would be as long as the list of "all even numbers" because any list of primes immediately gives you a next prime that should be on the list, but isn't, in the same way that having a list of even numbers immediately gives you the next even number that should be on that list but isn't: Given an ordered list of primes {2,3,5,...,n} one (of several) immediately known next prime number is simply (2 x 3 x 5 x ... x n) + 1. We know that number's prime because it cannot be cleanly divided by 2, or 3, or 5, or ..., or n. As such, even if it might be useful to have a list of all known primes, annotated with what kind of prime each number is, such a list cannot be constructed: even just the subset of all prime numbers generated based on the simple above rule would be infinitely long, just like the list of all even numbers is infinitely long.
- kryptiskt 9y agoRSA encryption keys uses the product of two large primes, where each prime is many digits long. So many new primes are "discovered" every day.
- schoen 9y agoInterestingly, those primes' primality is normally proven statistically rather than deductively. This is not really a practical issue for people using RSA, but could be a philosophical issue for someone interested in the question of how many different numbers' primality has been proven by humanity.
- madez 9y agoThere is rarely a submission here on Hacker News that has comments of such bad quality as this submission has. I see a similar phenomenon with press. They "hype" something they barely understand, change parts of the story to make it more interesting, or invent new words (Cyber!). This is a disservice. What do you do to avoid this noise?
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- dghughes 9y agoPrime numbers are amazing. I was watching a math documentary and one example was a Cicada in North Carolina that only emerges once every thirteen years millions of them at once. It's a defense mechanism the sheer number overwhelms predators. The Cicada does this also to avoid appearing when another species of Cicada appears to prevent cross breeding. The other species in the same region emerges every 7 years. The two will only emerge at the same time every 220 years (I think it as). Smart bugs!
- sidhack 9y agoIs this the 3-part BBC documentary - "The Code"?
- dghughes 9y agoYes I think that's what it is.
- Retr0spectrum 9y agoI vaguely remember watching the same documentary, so I don't doubt you. But surely they would emerge at the same time every 21 years? Edit: I looked it up, its 13 and 17 years, giving a 221 year overall cycle. I guess it only really "matters" that the years are coprime. https://en.wikipedia.org/wiki/Periodical_cicadas https://en.wikipedia.org/wiki/Periodical_cicadas
- jweather 9y agoThis is a similar concept to the odd numbers of teeth used in gear chains. If you had an 8-tooth and a 16-tooth gear, they will wear unevenly as the same teeth (with potential manufacturing defects) always meet the same teeth. If you change that to 7-tooth and 17-tooth, they will only repeat pairings every 119 teeth and wear will be distributed evenly across all teeth. In general, tooth numbers that are relatively prime (sharing no divisors) are preferred.
- WhitneyLand 9y agoBut why? One answer is a bit buried in a sub link in the article. On that page, you’ll find arguments for the following reasons: tradition, by products of the quest, collection of rare mathematical things, glory, pushing hardware performance, and contest rewards. Personally I’m forced to admit I enjoy seeing them found while being unable to form any cogent justification. http://primes.utm.edu/notes/faq/why.html http://primes.utm.edu/notes/faq/why.html
- yjftsjthsd-h 9y ago"Because it's there." - George Mallory
- yarg 9y agoThey're a nice source of mathematically justifiable entropy.
- vortico 9y agoThat's actually a fairly complete and accurate list of reasons for such a project. If I was interested, I'd do it for about half of those reasons, and others may prefer the other half.
- samstave 9y agoI know that humans want to know these things, but can someone ELI5 why this important?
- qmalzp 9y agoConsider it something like a benchmark of human progress.
- jbgreer 9y agoTIL I work at the same company as the discoverer of the 50th known Mersenne Prime. I know at least one sysadmin who used GIMPS as a burn-in program for new servers.....
- chrismorgan 9y agoIt’s common for stress-testing overclocking, too: https://en.wikipedia.org/wiki/Prime95#Use_for_stress_testing https://en.wikipedia.org/wiki/Prime95#Use_for_stress_testing
- wanderfowl 9y agoI use Prime95 to test for usage-related recording lags for sound and video recording in our lab equipment. If we're not getting signal de-synchronization with that slamming the CPU(s), we can worry a bit less.
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- sohkamyung 9y agoCurious: can bitcoin mining rigs be modified for BOINC projects (GIMPS, Seti@Home, etc.)? If yes, than I might invest in some rigs and modify them to run BOINC. Yes, I'm weird: I prefer to do computation for BOINC than for bitcoin. :-)
- tribby 9y agonowadays bitcoin mining rigs use ASICs that are optimized for the task, so I don't think that would be a good idea. on a general purpose system you can use GPUs and BOINC with SETI, not sure about GIMPS.
- sohkamyung 9y agoI see. Thanks. I do have some PC systems but they are shared among family members, making it difficult to run BOINC as a background task without interfering with their work. I'll look at low-cost systems, like the Raspberry Pi, to see if I can use them as dedicated BOINC boxes instead.
- schoen 9y agoIndeed, Bitcoin ASICs are not only "optimized" for the Bitcoin mining task (computing a particular hash function), they usually literally don't include the logic to perform other general-purpose computations at all! That's a big contrast with GPUs. There have been interesting discussions about a cryptocurrency whose proof of work task would be something in some way more interesting or more useful than partial hash collisions, but I don't think many such systems have caught on. There is a prime-related one called Primecoin: https://en.wikipedia.org/wiki/Primecoin https://en.wikipedia.org/wiki/Primecoin So, I guess that's a precedent for creating new cryptocurrency designs that do something else. I don't know if there's a way to make any of the BOINC tasks into cheap-to-verify PoW systems or if anyone's tried to do so, but that might be a cool project.