7 ms·
A New Largest-Known Prime Number
- burtonator 8y ago.
- thestoicattack 8y agoTwo is prime.
- zahreeley 8y agoAccording to German science magazine 2 is not prime
- deleted 8y ago[deleted]
- heyjudy 8y agoThat's not a primary source and wrong. A prime is most simply: it has no factors other than itself and 1. "Not being even" is a corollary, and would be redundant if included in the definition of primality.
- adtac 8y ago>That's not a primary source Heh.
- schoen 8y agoAnother way to see this is to observe that the Fundamental Theorem of Arithmetic would be wrong (or more difficult to state succinctly) if 2 were not considered prime or if 1 were considered prime. For example, if 2 were not prime, it would be impossible to represent the number 256 (or the number 123456) as a product of primes.
- throwawaymath 8y agoThis is an excellent rebuttal, nice.
- lurchedsawyer 8y agoIt's not, though. It's one group of mathematicians appropriating prime numbers and jack-booting them into their favourite theorem. There are valid reasons to treat 1 as a prime number, just as there are for defining 0^0 as 1 in some cases. Also for a fun pastime try asking an arithmetician to apply the fundamental theorem to 1 and watch them squirm.
- schoen 8y agoPresumably the arithmetician will answer that its factorization is the empty set. That's what sympy says, for example. >>> sympy.factorint(6) {2: 1, 3: 1} >>> sympy.factorint(1) {} This definition is also sensible because it also preserves uniqueness in both directions. The empty set is the only prime factorization of 1, and 1 is the only natural number whose prime factorization is the empty set. (Wikipedia has a footnote that "Using the empty product rule one need not exclude the number 1 [from the fundamental theorem of arithmetic], and the theorem can be stated as: every positive integer has unique prime factorization.") The fundamental theorem doesn't have to state that the prime factorization is nonempty. It's true that some mathematicians have defined 1 as a prime number and there's nothing logically inconsistent about doing so, but it makes most theorems and formulas in number theory more complex and so this definition has fallen out of favor. Edit: I think the Wikipedia article on the empty product gives some quite nice examples of the benefits of a closely related concept. https://en.wikipedia.org/wiki/Empty_product https://en.wikipedia.org/wiki/Empty_product
- lurchedsawyer 8y agoSee? Squirming. Somehow multiplying 0 factors is supposed to result in 1. I'm not saying it's incorrect, but you have to explain that edge case away. At the same time allowing 1 to be prime would remove that problem given that e.g. 6 = 2^1 * 3 ^1 and 6 = 1^81 * 2^1 * 3^1 are the same unique factorisation because, well, monoids. Edit: `s/fields/monoids`
- revskill 8y agoNumber Theory is beautiful, but impractical for daily usage or programming. Who cares ?
- dang 8y ago"Please don't post shallow dismissals, especially of other people's work. A good critical comment teaches us something." https://news.ycombinator.com/newsguidelines.html https://news.ycombinator.com/newsguidelines.html
- zahreeley 8y agoBut who asked to do such wasteful work?
- Cyph0n 8y agoThat may be true now, but perhaps not in the future. Heck, mathematicians in general thought number theory was “useless” up until only around 40 years ago. Now we know that our world could not have developed this way without the creation of modern cryptography. I think number theory serves as a great example for why basic research is so important to humanity.
- heyjudy 8y agoWow. I can't believe having to explain curosity or that other people have uses for things that some people don't understand. Smh.
- zahreeley 8y agoYep I also don’t care. It’s a waste of time.
- throwawaymath 8y agoImpractical for daily usage? Surely you use TLS daily, in some fashion, do you not?
- delhanty 8y agoRead this and wondered, what estimates are there on the density of the Mersenne primes as n grows? Google told me that, surprisingly, it's not even known that they are infinite! I found this nice page on the Wagstaff Mersenne Conjecture: https://primes.utm.edu/mersenne/heuristic.html https://primes.utm.edu/mersenne/heuristic.html
- ryacko 8y agoPossibly the only civilian use of quantum computing, an interesting decade is ahead.
- scythe 8y agoPrimality testing is actually much easier than integer factorization thanks to Fermat's "little" theorem. Methods based on this theorem, including the Lucas-Lehmer test for Mersenne primes, can identify prime numbers on classical computers in polynomial time. However, factorization is not possible with this method.
- chris_st 8y agoThat's okay, hardly anyone needs to factor prime numbers :-)
- man-and-laptop 8y agoIt would be nice if this were used as the PoW problem for a blockchain. Since the Mersenne Primes are rare, the PoW problem shouldn't be to find new Mersenne Primes directly, but something that could make indirect progress on that. Also the blockchain should solve an actual problem, such as torrent tracking or DNS. It makes me think that there should be a list of viable uses of blockchain, and another list of interesting problems that could be moulded into PoWs, and they should be paired up into blockchains.
- _trampeltier 8y agohttps://gridcoin.us/ https://gridcoin.us/
- bulka 8y agoHow would you measure amount of work you want to reward with a coin? In both DNS and torrent examples one can influence a supply of work to be done rather easily
- man-and-laptop 8y agoIt's a broad idea to construct a secure PoW, with all that's required to make it secure, but to try and make it applicable to areas like number theory. See PrimeCoin for a successful example. Also your concerns are unfounded: See Namecoin and Primecoin. I'm thinking these two ideas could be combined.
- topmonk 8y agoOne problem is that a black hat could solve a lot of primes in secret, and then use those for a double spend attack. Specifically, a) Spend some coins to buy some other cryptocurrency b) use all their secret primes creating a bunch of new blocks on a branch where they haven't spent their money. Since this is the longest branch now, all the other clients accept they haven't really spent it. c) buy the other cryptocurrency again on this new branch.
- man-and-laptop 8y ago
- zahreeley 8y agoWhy we are after Prime numbers and not to discover where soul goes after death?
- swampthinker 8y agoPerhaps they are related.
- zahreeley 8y agoHehe
- spiritcat 8y agoyou mean like like each prime makes up one of the unique universal souls that exist throughout time and space? whoa
- heyjudy 8y agoThe universe is likely a simulation, so a soul maybe a prime primary key and so use a Mersenne prime to save space as a form of compression because only n needs to be stored, not the full bitstring. The real question is: does the universe have microcode opcodes to operate on Mersenne primes natively without expanding them? PS: Atheist ;)
- 2stop 8y agoLikely a simulation... Even though there isn't any empirical evidence of this fact... But you still believe? Is athiesm just another form of religion these days?
- AnimalMuppet 8y agoIf the universe is a simulation, isn't the programmer effectively God? And: "Likely"? Objection, your honor. Assumes facts not in evidence.
- 8y ago
- heyjudy 8y agoMersenne primes in binary are all 1's with length n. PS: I remember scheduling Prime95 to run on lab computers at work (a nuclear engineering shop) after-hours, c. 1998.
- zozbot123 8y agoNow for the real question... is this good for Primecoin?
- eximius 8y agoAnyone know what primality test they use? Miller-Rabin for testing then something deterministic for verification?
- ehsankia 8y agoThey use Lucas-Lehmer's[0] which is specifically for Mersenne primes[1] https://www.mersenne.org/various/math.php#lucas-lehmer https://www.mersenne.org/various/math.php#lucas-lehmer https://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_primality_test https://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_primality...
- fluxty 8y agoI used to be into this stuff in college--we were obsessed with the idea of generating very large or else very large numbers of odd numbers, such as weird numbers or untouchable numbers. I was into HPC and writing programs that run on clusters, and this gave me some good practice. We eventually realized that no one really cared about the numbers we felt confident we could find--now Mersenne primes, though, people really care about those, but they're extraordinarily difficult to find. Always a cool day to see a new one.
- AlexCoventry 8y agoIt's not clear to me that anyone really cares about Mersenne primes, either, which is not to detract from this cool result in any way.
- JewsDidIt 8y agoI'm particularly a fan of 1,000,000,000,000,066,600,000,000,000,001.
- userbinator 8y agoWe would write the number out for you, but it would fill up thousands of pages, give or take, and look like this gigantic zip file. It's ironic to see that 11MB file being called "gigantic" in this day and age; many web pages are now unfortunately much larger, and the page of the article itself transfers at least 1MB of data.
- anoncoward111 8y agoUnironically this. NPR even has a subdomain for text only (text.npr.org), but only select articles are ported because reasons. A thorough joke.
- carlob 8y agoThen it's probably in decimal form. The binary representation should compress much better :)
- dvh 8y agoAny number N in base (N) is written as 1
- carlob 8y agono it's 10
- SomeHacker44 8y agoTypical programmer. Off by zero as always.
- paulddraper 8y agoExplanation: A Mersenne prime is (2^n)-1 so in binary that's n 1s.
- NKosmatos 8y agoThe official press release from GIMPS: https://www.mersenne.org/primes/?press=M82589933 https://www.mersenne.org/primes/?press=M82589933