[HN Gopher] New Mersenne Prime discovered (probably)
       ___________________________________________________________________
        
       New Mersenne Prime discovered (probably)
        
       Author : sdsykes
       Score  : 329 points
       Date   : 2024-10-16 11:51 UTC (3 days ago)
        
 (HTM) web link (www.mersenne.org)
 (TXT) w3m dump (www.mersenne.org)
        
       | jmclnx wrote:
       | Nice and tentative congratulations.
       | 
       | I use to run Mersenne Prime Search (GIMPS), but now all I have is
       | laptops. It runs to hot on the Laptops I have :(
       | 
       | Will need to play with throttling some more.
       | 
       | Edit: found mprime (mprime-bin-24.14) is available in NetBSD
       | pkgsrc. But this uses 32 bit linux emulation to execute, I have
       | been trying to avoid it, but may try it.
        
       | ziofill wrote:
       | I can swear something like 20+ years ago I found a new one too,
       | but I didn't realize the importance of it. I had just downloaded
       | GIMPS and I was just messing around with it, and when I saw the
       | message I thought "ok, cool!" and proceeded to turn it off.
        
         | lifthrasiir wrote:
         | Do you have any slightest idea about the exponent, including
         | how many digits in the exponent? I assume you had no account
         | (otherwise there should have been some logs for that).
        
         | therein wrote:
         | I'd believe it. Many years ago when I was around 10 years old
         | and not understanding the concept of probability properly, I
         | decided I had come up with a way to enumerate the lottery
         | numbers and come up with a reasonably sized set of numbers to
         | place bets for. I proceeded to write 9 pages of numbers for my
         | father to place bets for. It is a 6/49 lottery so 6 balls are
         | drawn from a set of 49 and you need to get all of them right to
         | get the jackpot.
         | 
         | It would have cost a little under 95$ to have played all my
         | numbers (for a jackpot around $1.5M) I gave him however it
         | would have taken a lot of effort to manually enter them. My
         | father just does one page because it is silly. The numbers are
         | silly, everything about this is silly. I completely understand
         | in hindsight. But it turned out page 7 had the winning
         | combination.
        
           | Jerrrry wrote:
           | I've seen that movie too
        
           | Nition wrote:
           | I'm not sure why your comment is currently downvoted, you're
           | not claiming it was anything but random luck and it's a funny
           | story. Thanks for sharing.
        
           | ashleyn wrote:
           | If the balls were improperly weighted at the lottery
           | commission, then maybe you'd have unwittingly discovered the
           | bias in the game. That's certainly possible.
        
         | schoen wrote:
         | If it was literally around "20+ years ago", like 2004 or
         | slightly before, it might have been M40 or M41.
         | 
         | https://en.wikipedia.org/wiki/List_of_Mersenne_primes_and_pe...
         | 
         | If this happened the way you remember, it's really unfortunate,
         | but it wouldn't have stopped the prime in question from being
         | discovered, because GIMPS always at least eventually gives out
         | numbers to multiple people to check, and doesn't mark Mersenne
         | numbers as checked until a computer actively reports that they
         | were checked.
         | 
         | However, your name could have ended up on that Wikipedia list
         | as a discoverer. :-)
        
           | aphantastic wrote:
           | Interesting that all the primes since 2001 have been
           | discovered by Intel processors (at least those where the
           | processor was recorded). How's that for marketing?
        
             | Jerrrrrrry wrote:
             | If bitcoin used a facet of primality in its Proof-of-Work,
             | that would nearly needlessly gloating.
             | 
             | But it doesn't, and unfortunately even worse, it wasn't
             | ASIC-resistant, which had second-order effects that Intel
             | could had actually taken advantage of if they werent
             | sleeping from being too comfortable.
        
               | freeqaz wrote:
               | Is there a good POW mechanism that would test primes?
               | 
               | I found this but curious what else exists!
               | https://en.wikipedia.org/wiki/Primecoin
        
               | Jerrrrrrry wrote:
               | Thats it (afaik), and it could be for the usual,
               | dismissive reasons, but its easy to hand-waive the "make
               | primality a part of the work" part but it also comes down
               | to the properties of the work that require it to be
               | useful:
               | 
               | the difficulty of the work must be adjustable,
               | 
               | the difficulty/reward ratio must scale to the polynomial
               | of users/work-rate to avoid sybil/"51% (31%)" attacks,
               | and dissuade volatility during transitions
               | 
               | must be easily verifiable,
               | 
               | Primecoin uses Cunningham Chain primes - basically
               | sequences of primes where 2x+1 is prime.
               | 
               | They are marginally useful with other applications on the
               | horizon.
               | 
               | I could see adjusting the arbitrary rule-set - similar to
               | the varying rulesets of cellular automata, like Conways -
               | to further Number Theory/Game Theory/Swarm Economics at a
               | general interdisciplinary level to be the most
               | potentially rewarding, covering a larger swath of unknown
               | unknowns.
        
               | aphantastic wrote:
               | My favorite "Practical POW" remains komoglorav complexity
               | computation. The reward would likely scale with the
               | runtime needed to verify a complexity, but there's plenty
               | of room for subtleties in the implementation. (for
               | instance what happens when you prove a prior established
               | complexity wrong?)
        
               | Jerrrrrrry wrote:
               | >(for instance what happens when you prove a prior
               | established complexity wrong?)
               | 
               | what do you mean? you run their wallets, pun intended!
               | 
               | No stakes, no steaks!
               | 
               | But it does seem interesting - counterintuitive really,
               | but a "Busy Beaver" / proof of work verifying mechanism
               | enumerating inputs/instructions/outputs randomly (or
               | whatever the nodes think they know best at ) while
               | rewarding (only? why not top 3?) the shortest, most
               | efficient block...could be tweaked to crunch ETH
               | contracts like gas, brute-force fuzz-test legacy unsafe
               | sourcecode...literally a foundation for further
               | distributed computation.
               | 
               | There are languages like it - Dennis and his Bubblegum -
               | that have generative, selective, and compressive patterns
               | interned already.
               | 
               | https://esolangs.org/wiki/Bubblegum
        
               | tromp wrote:
               | You forgot one important property: it must commit to the
               | new block(header).
        
               | tromp wrote:
               | There's also https://gapcoin.org/ for searching prime
               | number gaps (mine the gap).
        
               | Jerrrrrrry wrote:
               | I knew I forgot something, thank you!
               | 
               | 10 years!
        
               | tromp wrote:
               | There's also https://riecoin.xyz/ searching prime
               | constellations.
        
               | dgacmu wrote:
               | Primecoin (Cunningham chains)
               | 
               | Gapcoin (finding large gaps between successive primes)
               | 
               | Riecoin (finding maximally dense prime clusters of size
               | 6)
               | 
               | Nexus (finding almost-dense clusters with a maximum
               | spacing between successive primes)
               | 
               | As an aside, picking a mathematically interesting and
               | intricate proof of work function is probably a bad idea,
               | because someone like me will come along and optimize the
               | miner and mine privately at a large profit margin, as I
               | did with two of these coins.
        
               | einpoklum wrote:
               | Don't forget:
               | 
               | Primemarkcoin
               | 
               | Perceptiongapcoin
               | 
               | Liecoin
               | 
               | epiplexiscoin
               | 
               | and of course, the every useful pyramidcoin and scamcoin.
        
               | zeven7 wrote:
               | This reminded me that I used to leave my computer running
               | Folding@home or similar projects around 2010-2011. Not
               | sure if it ever contributed to anything. If only I had
               | known to run a Bitcoin miner instead!
        
               | tirant wrote:
               | Back in 2009-2010 I was responsible for deploying 8-16
               | core servers to customers to run large databases and
               | ERPs. I had the idea of doing some burn in testing to
               | stress the components for around a week for each server.
               | Back then I was aware of bitcoin but also SETI@home.
               | Obviously I chose the second option as I believed it was
               | probable my a better choice for humans kind. It obviously
               | was, but bitcoin mining would have been a better one for
               | me.
        
               | omgwtfbyobbq wrote:
               | I remember some rough calculations suggested I needed to
               | upgrade from agp to pcie to make bitcoin mining worth it
               | financially. I went with boinc instead.
        
               | andrepd wrote:
               | I remember calculating that the 0.08 btc that I was
               | mining per day on my desktop wasn't worth the
               | electricity.
        
               | lupire wrote:
               | That's exactly how Bitcoin is designed to autobalance.
               | It's only worthwhile if you believe demand will increase
               | in future.
        
               | JKCalhoun wrote:
               | I ran the SETI software as well. Was not Bitcoin
               | mining....
               | 
               | I suspect neither your or I though have ever had to turn
               | over a landfill looking for a hard drive. So there's that
               | anyway.
        
               | shawnz wrote:
               | The work in a PoW algorithm has to be otherwise useless
               | in order for it to most effectively deter abuse, or else
               | you'd still be able to get value out of failed attack
               | attempts
        
               | loup-vaillant wrote:
               | What second order effect are you referring to? Stuff like
               | manufacturing, or fab availability perhaps?
        
         | rollinDyno wrote:
         | Hey at least you weren't one of those kids who ran into those
         | online faucets that were giving bitcoins for free and didn't
         | think too much about it.
        
           | Jerrrrrrry wrote:
           | its like "the game" but you feel like you got stabbed by
           | Hindsight herself
        
           | stavros wrote:
           | I remember the faucet giving 5 BTC to play with. I still have
           | my wallet history from those days, with transactions of
           | multiple millions (today) in BTC between wallets and friends.
        
         | Aurornis wrote:
         | > I had just downloaded GIMPS and I was just messing around
         | with it, and when I saw the message I thought "ok, cool!" and
         | proceeded to turn it off.
         | 
         | GIMPS would run for weeks or months first. You wouldn't have
         | seen anything if you had just downloaded it and were messing
         | around. As I recall, you had to do some work to get it running
         | at boot automatically.
        
           | stavros wrote:
           | Does it take months to check one prime? Maybe the author got
           | extremely lucky.
        
         | solardev wrote:
         | I thought this was about GIMP at first, the GNU Image
         | Manipulation Program. Like did they hide a prime number check
         | into the brush strokes algorithm so users would become
         | pseudorandom generators whenever they made art...? And you just
         | happened to draw the right thing that also happened to be a
         | prime?
         | 
         | But nope, it's just a similar acronym!
         | https://en.wikipedia.org/wiki/Great_Internet_Mersenne_Prime_...
        
           | nbbaier wrote:
           | I absolutely had the same thought progression
        
       | beyondCritics wrote:
       | Great news for humanity.
        
         | hyperhello wrote:
         | We get free two-day shipping on our Mersennes.
        
           | xanderlewis wrote:
           | Thanks, Jeff!
        
       | dooglius wrote:
       | Why don't they say what it is?
        
         | CamperBob2 wrote:
         | Or even the number of digits.
        
         | lifthrasiir wrote:
         | Because the EFF Cooperative Computing Awards for the first
         | discovery of large enough prime numbers are still active.
         | Publishing the probable prime in advance would risk someone
         | verifying faster than GIMPS.
        
           | Dylan16807 wrote:
           | It's hard to see how that someone would count as the
           | discoverer.
        
             | lifthrasiir wrote:
             | That someone will totally count as the discoverer under the
             | current rules [1], because it requires the deterministic
             | primality proof for given number. It doesn't matter how
             | much effort was taken to reach that candidate so far, even
             | though it would be virtually impossible to find any new
             | prime without that. I think the temporary embargo is fully
             | justified for this reason.
             | 
             | (And I think it is technically possible to probe the
             | reports to find what it was anyway, but it is not easy to
             | find one at least for me. If you are really looking for
             | that, look for the P-PRP result type.)
             | 
             | [1] https://www.eff.org/awards/coop/rules
        
               | phkahler wrote:
               | Is there a probabilistic test for Mersene primes? I
               | thought they just wanted confirmation via independent
               | calculation.
        
               | lifthrasiir wrote:
               | Any probabilistic primality test will work, but GIMPS
               | currently uses the first-time Fermat probable prime test
               | with a very robust certificate [1] to filter almost all
               | non-primes in advance.
               | 
               | [1] https://www.mersenne.org/various/math.php#prp
        
             | Jerrrrrrry wrote:
             | How hard?
             | 
             | NP hard?
             | 
             | I wonder why?
             | 
             | :)
        
           | schoen wrote:
           | I used to run the Cooperative Computing Awards, and I don't
           | think this is the reason in this case.
           | 
           | The most recent award was given out in 2009 for a prime over
           | 10,000,000 digits in length. The next available award is for
           | a prime over 100,000,000 digits in length.
           | 
           | But the most recent discovery by GIMPS prior to the current
           | discovery was a prime with length only 24,862,048.
           | 
           | https://en.wikipedia.org/wiki/List_of_Mersenne_primes_and_pe.
           | ..
           | 
           | The primes they've found have been getting longer by only
           | single millions of digits every several years, so it's not
           | very plausible that this discovery would qualify for a
           | monetary award.
           | 
           | I suspect they just don't want to announce a number before
           | it's verified on general scientific-integrity grounds.
        
             | lifthrasiir wrote:
             | GIMPS currently searches for exponents up to 999,999,999,
             | corresponding to 301,029,996 decimal digits. We don't
             | really know much about the exact distribution of Mersenne
             | primes so it is possible that a new discovery was from much
             | higher ranges and thus eligible for prizes.
             | 
             | But yeah, they'd probably embargoed even without any
             | potential monetary prizes because it's wise to do so in
             | general ;-)
        
               | schoen wrote:
               | Sure, but all actual historical discoveries of Mersenne
               | primes since the 1980s have been in strictly increasing
               | size order, with no missed primes in between found in
               | retrospect, and the successful exponents have increased
               | gradually rather than sharply in size. It would _really_
               | buck the trend to an extreme degree if the new successful
               | exponent were 5x as large rather than something like
               | 1.05x as large as the previous record.
               | 
               | I want to make an analogy to sports records, but the
               | analogy will obviously be imperfect because the limits of
               | human physiology are better understood in some ways than
               | the behavior of Mersenne primes and perfect numbers. But
               | it might be like if we heard that the marathon record had
               | been beaten and then it turned out that the new record
               | was something like 1:30:00 instead of something like
               | 2:00:00. Obviously the exact value of the new record is
               | totally unpredictable, but the best bet is that something
               | like long-term trend lines will continue to be followed,
               | rather than abruptly radically changed by multiple orders
               | of magnitude.
        
               | lifthrasiir wrote:
               | M43112609 (2008-08) was discovered prior to M42643801
               | (2009-06), so that order is not really strict. I agree
               | that there is a human tendency to test smaller primes
               | (thus faster to verify) first, but it should be also
               | noted that every single Mersenne number smaller than
               | M124399361 has been already tested at least once by
               | someone even though that limit would be way higher than
               | what we have for primes. There are also some groups of
               | people that specifically look for prime numbers that are
               | barely enough to be 100,000,000+ decimal digits [1].
               | Given we didn't see any new Mersenne prime for many
               | years, new prime from a random range seems much more
               | likely than ever.
               | 
               | [1] See https://www.mersenne.org/primenet/ and scroll
               | down to the starting exponent of 332,000,000. There would
               | be an unusually large number of assigned LL/PRP tasks
               | around this range. In fact, this holds for virtually all
               | available PrimeNet statuses in the Wayback machine!
        
               | Jerrrrrrry wrote:
               | Sports analogies are good, but:
               | 
               | Any% (Anything goes to get to the "end") Video game
               | speedruns may be ideal - a shortcut can always be found,
               | used by everyone to quickly become zero sum + 1, then the
               | equilibrium re-approaches optimization; but on average,
               | gets harder and harder, as the shortcuts take
               | skill/power/time. It also is hard to do, and easy(ish) to
               | verify.
               | 
               | For linear things that hardly have any variance, you can
               | look at longest lifespans of humans. Notably; where
               | living 18 months longer than the next person
               | statistically makes it more likely that you are actually
               | your own mother and lied.
        
           | gus_massa wrote:
           | How do you prove that you verified that a number is a prime?
           | 
           | If you want to prove that a number is not a prime you can
           | show the factorization or that it breack the little theorem
           | of Fermat with 367984321568, and everyone can check the
           | refutation inmediately.
           | 
           | I don't know a similar method to show that you actualy
           | verified the number is a prime.
        
             | ColinWright wrote:
             | There are primality proving certificates.
             | 
             | https://en.wikipedia.org/wiki/Primality_certificate
             | 
             | These are sometimes infeasible for stupidly big numbers,
             | but the Mersenne Primes have a specific structure that
             | allows for simplification of the process.
        
       | MPSimmons wrote:
       | Time for Bruce Schneier to change the combination to his luggage
       | again
        
         | schoen wrote:
         | For anyone who didn't get the joke, this is a reference to
         | 
         | https://www.schneierfacts.com/facts/365
         | 
         | from the "Bruce Schneier Facts" series (which was inspired by
         | the "Chuck Norris Facts").
        
           | m463 wrote:
           | looking at the picture, I imagine it's like a zero day when
           | you can "enter the drag-on'
           | 
           | (it's like a prime protected carry-on that schneier carries)
        
           | winwang wrote:
           | thank you for the education :) this is so good!
        
           | fhars wrote:
           | Not 137? https://www.schneier.com/blog/archives/2005/06/picki
           | ng_physi...
        
             | Waterluvian wrote:
             | It's not quite 137, though. The last digit needs to be oh
             | so slightly off.
        
         | hinkley wrote:
         | Luggage that would make Dan Brown green with envy.
        
           | throwawee wrote:
           | Needlessly confusing if Dan Brown is green and Dan Green is
           | white. Somebody standardize Dans.
        
             | onionisafruit wrote:
             | Danny White is white, so that's a start
        
       | natas wrote:
       | Chuck Norris has already discovered and factorized all the prime
       | numbers.
        
         | toast0 wrote:
         | A number is prime if its factors are itself, one, and Chuck
         | Norris.
        
           | dudeinjapan wrote:
           | A number is prime if it is the number of times Chuck Norris
           | roundhouse kicked Optimus Prime
        
       | ramshanker wrote:
       | Awesome. I have been recommending in my organization, 24 Hrs.
       | Prime95 Stress Test as part of acceptance protocol for all new
       | servers ! Happy to see it find another record Mersenne Prime.
        
         | 0xDEADFED5 wrote:
         | y-cruncher is the king of stress testing
        
       | dudeinjapan wrote:
       | Hell yeah!! This is the best thing to happen all week!!!
        
       | Eliezer wrote:
       | lol, like the government doesn't have 3 more Mersennes they keep
       | secret so they can verify potential First Contact situations
        
         | Jerrrrrrry wrote:
         | the idea of a deep-nation-state-cold-war psyop campaign
         | bluffing and escalating math proofs is so goddamn hilarious,
         | apt, and ironic it would be almost better than the mistake of
         | pissing off the Aliens by offending them with math homework.
         | 
         | "Shizuo Kakutani joked that the problem [Collatz conjecture]
         | was a Cold War invention of the Russians meant to slow the
         | progress of mathematics in the West."
        
         | jiggawatts wrote:
         | They're much easier to verify than to find. Just ask for the
         | next one hundred unknown primes and check the response.
        
           | Jerrrrrrry wrote:
           | This still suffers from the MitM / Two Generals Problem, and
           | is existentially problematic if they also demand the simple,
           | reasonable sum of the first BB(17) numbers modulo Grahams
           | number, within 14 business local parsec-years.
           | 
           | Their spam filter may be an annoying ping acknowledgement, a
           | directed gamma ray beam from soft gamma repeater, just to
           | irradiate their own hoax-doers suspects.
        
       | dataflow wrote:
       | Given this contest can presumably go on infinitely long, what is
       | the ultimate point of the contest? Is there some kind of
       | theoretical or practical benefit to discovering a new Mersenne
       | prime?
        
         | artursapek wrote:
         | It's exploration of new lands
        
         | ISL wrote:
         | To learn something about primes.
         | 
         | Perhaps there is a pattern or a way to more-accurately predict
         | which numbers will be prime.
         | 
         | Also, it is cool.
        
           | mort96 wrote:
           | Do we expect to learn something interesting from any given
           | new Mersenne prime discovered? Don't we kinda have enough so
           | that if we are going to discover something interesting by
           | analyzing them, we can do that with the ones we already know
           | about?
        
             | lagadu wrote:
             | I'm not an SME but I would imagine that if there's some
             | sort of very large scale pattern in Mersenne primes then
             | finding that might lead to the discovery of some currently
             | unknown emergent property. Of course this argument is
             | likely unfalsifiable, as it can scale infinitely if there's
             | an infinite amount of them, though we don't even know
             | whether they are a finite set or not.
        
             | tomtomtom777 wrote:
             | Isn't the fact that a certain number is a Mersenne prime
             | interesting in itself? Surely it's a great addition to our
             | knowledge of numbers?
        
               | mort96 wrote:
               | Sure, I'm not against GIMPS or anything, I'm just a bit
               | doubtful that finding a few more Mersenne primes could be
               | the key to unlocking some secret pattern in the primes is
               | all
        
         | schoen wrote:
         | The EFF Cooperative Computing Awards, which pay out money for
         | (four specific sizes of) prime records, were meant to show off
         | how the Internet is useful for letting people who don't even
         | know each other work together to solve problems. They were
         | established back in 1998, when people in general were _much_
         | less familiar with the Internet and its impact. That specific
         | contest isn 't set up to go on forever, as it ends when a
         | billion-digit prime is discovered.
         | 
         | The search for different kinds of mathematical objects
         | sometimes has applications and sometimes doesn't. For example,
         | apparently the search for Golomb rulers (another distributed
         | computing project) has some conceivable applications.
         | 
         | https://en.wikipedia.org/wiki/Golomb_ruler#Practical_applica...
         | 
         | There's a misconception (that I heard dozens or hundreds of
         | times when I was running the Cooperative Computing Awards at
         | EFF) that discovering world record primes is useful to
         | cryptography. In fact, it has no direct application because all
         | of the primes used in number-theoretic algorithms like RSA and
         | classic Diffie-Hellman are _dramatically_ smaller than world-
         | record sizes, and can be generated on an ordinary PC in
         | seconds. (Try  "openssl prime -generate -bits 2048" at your
         | command line!)
         | 
         | (There is a wild paper from 2017 called "Post-quantum RSA"
         | arguing that we could in principle just scale up RSA keys for
         | post-quantum security, but that paper uses multiprime RSA
         | moduli composed of large numbers of 4096-bit primes, instead of
         | just the traditional two primes, so even that approach doesn't
         | require individual primes that are especially large or hard-to-
         | find by computer standards.)
         | 
         | We have apparently learned a bit about number theory and
         | algorithms as a result of research done by the GIMPS project
         | and its collaborators about how to optimize some of the
         | arithmetic in the GIMPS client. I guess that's the equivalent
         | of the claim that the space program produced various spin-off
         | technologies while pursuing space exploration.
         | 
         | In general, since there are infinitely many primes, there's no
         | reason that humanity can't keep looking for larger and larger
         | ones indefinitely. Likewise for many other searches, both for
         | objects which are known to be infinitely numerous and objects
         | which may or may not have a largest example. Mostly this kind
         | of activity has a "because it's there" flavor to it.
         | 
         | https://en.wikipedia.org/wiki/George_Mallory
         | 
         | Research mathematicians are mostly not that excited about this
         | activity, because it isn't generating more understanding or
         | hypotheses about mathematical structure. They're usually more
         | excited about insights that reveal or hint at new patterns or
         | structure, which searching for large primes doesn't really do
         | (most of the work is mechanical, performed by computers, and
         | the outputs aren't very surprising or suggestive in a
         | mathematical sense).
         | 
         | I've hoped that publicity about discoveries like record primes
         | might get more young people interested in mathematics (and
         | maybe about topics like number theory and discrete math that
         | they might not be encountering in school). I got kind of a sad
         | view of this because people were constantly writing to me
         | asking for monetary rewards for their inevitably-mistaken-or-
         | confused "discoveries", but I'd like to think that there are
         | also people out there who got curious about what we do and
         | don't know about primes. A good place to start with that is the
         | Prime Pages
         | 
         | https://t5k.org/
        
           | fhars wrote:
           | And wasn't that paper just poking fun at people who still
           | used something as outdated as RSA as the default public key
           | crypto primitive in the 2010s by extrapolating their position
           | to its logical extreme?
        
             | schoen wrote:
             | I think there was an intended humor element there,
             | particularly since some of those people were also working
             | on new post-quantum primitives, but they also "committed to
             | the bit" and did the research for real.
        
         | Jerrrrrrry wrote:
         | >presumably go on infinitely long
         | 
         | prove it
        
           | poincaredisk wrote:
           | It's well established that there are infinite prime numbers,
           | for example https://www-
           | users.york.ac.uk/~ss44/cyc/p/primeprf.htm
        
             | Jerrrrrrry wrote:
             | Should be able to trivially extend that logic to Mersenne
             | Primes then, 'presumably'
        
               | NeoTar wrote:
               | It's not.
               | 
               | The traditional proof that there are an infinite number
               | of primes relies on unique prime factorisation- i.e for
               | any number, n, there is a unique set of primes p1, p2,
               | p3, ... etc. where p1 * p2 * p3 * ... = n
               | 
               | For instance 88 = 2 * 2 * 2 * 11, 42 = 2 * 3 * 7
               | 
               | It's worth reading the proof if you haven't - it's
               | comprehensible with high school maths.
               | 
               | No such property exists for Mersenne primes, so we can't
               | trivially extend it. Many proofs of the properties of
               | prime numbers are difficult because they, by definition,
               | actively resist patterns.
        
           | dataflow wrote:
           | I didn't claim there are an infinite number of Mersenne
           | primes. I said the contest could presumably go on infinitely
           | long. The latter doesn't require the former. It's only
           | predicated on us lacking proofs about how many there must be.
        
             | Jerrrrrrry wrote:
             | >I didn't claim there are an infinite number of Mersenne
             | primes.
             | 
             | I didn't claim that you did, only that the contest...
             | 
             | you actually almost got me :)
        
               | dataflow wrote:
               | I mean, that's what I took from your comment here,
               | quoting my "presumably":
               | https://news.ycombinator.com/item?id=41888609
        
       | benreesman wrote:
       | I turned 40 recently and it was the only devastating milestone
       | before or since. No excuses: I blew that.
        
       | jl6 wrote:
       | Finally! Just when I thought everyone had moved their spare
       | compute to more lucrative schemes.
       | 
       | It's the longest wait for a new mersenne prime since the
       | discovery of M32 in 1992.
        
         | noduerme wrote:
         | amazing how many bitcoins have been discovered since then.
         | Satoshi should've incentivized mining something useful.
        
           | yreg wrote:
           | Are these high Mersenne primes all that useful?
        
             | gnramires wrote:
             | I've been thinking there should actually be more useful (or
             | at least more interesting? :P) crowd computing stuff.
             | 
             | How about something like Superoptimizing (with correctness
             | proofs) open source code?
        
           | iamgopal wrote:
           | every new prime for new block, but not linear.
        
       | stevefan1999 wrote:
       | But why do we have to "discover" it when we know the formula
       | would be 2^N - 1...? Are we trying to prove a corollary or what?
        
         | aaronmdjones wrote:
         | Not all 2^N - 1 are prime. For example, N=18 makes 2^N - 1 =
         | 262143, which can also be written as 3^3 * 7 * 19 * 73 (not
         | prime).
        
           | stevefan1999 wrote:
           | Oh, right, all Mersenne number is in the form of 2^N -1, but
           | Mersenne prime is Mersenne number plus being prime
        
             | mort96 wrote:
             | And we look for Mersenne primes, AFAIU, mainly because
             | Mersenne numbers are more likely to be prime than other
             | numbers, so it's easier to find big primes that way.
        
           | umanwizard wrote:
           | A lot simpler example is 2^4-1=5*3
        
             | lupire wrote:
             | 2^11-1 (prime power) for a less trivial example
        
         | Jabrov wrote:
         | There's tons of numbers of the form 2^N-1 which are not prime.
         | 
         | To discover the primes, we have to iterate through the numbers
         | and test their primality. With numbers that are so big, it's
         | very compute intensive
        
       | hockyy wrote:
       | https://oeis.org/A000043
        
       | sfelicio wrote:
       | If anyone is interested in knowing more, Veritasium has a good
       | video on this, "The Oldest Unsolved Problem in Math":
       | https://youtu.be/Zrv1EDIqHkY
        
       | sashank_1509 wrote:
       | I always wondered if we could parallelize a prime test on GPU.
       | That would give us a Datacenter level compute and really help us
       | scale, but it might be too hard to do.
        
         | 4gotunameagain wrote:
         | https://github.com/preda/gpuowl
        
       | p5a0u9l wrote:
       | Are there statistics on the scale of compute available to GIMPS
       | for this search? Is there any evidence that by crowdsourcing the
       | clients, we are searching faster than, eg, a dedicated cluster
       | financed by a government or a corporation? What is the impact of
       | GIMPS as a distributed problem solving tool? Like, if there was a
       | practical application, how much money would it take to exceed
       | GIMPS throughput, that curious people provide for free?
       | 
       | I'd like it to be astronomical, but given the niche of this, and
       | the low cost of cloud compute, the answer is predicable
       | depressing, like, "$50k/year in AWS costs would equal current
       | GIMPS search throughput"
        
         | mpreda wrote:
         | > "$50k/year in AWS costs would equal current GIMPS search
         | throughput"
         | 
         | I think you may be wrong by at least 3 orders of magnitude.
        
         | areyousure wrote:
         | https://www.mersenne.org/primenet/ suggests 127 PFlop/s average
         | over the last month, which would put it in the top 10 on
         | https://top500.org/lists/top500/2024/06/
         | 
         | I used a random estimate online for computing cost which had
         | 5.6e17 Flops per dollar on A100s gives about a dollar every 4.4
         | seconds or ~$7 million per year.
         | 
         | Sadly, I do not vouch for the correctness of any part of this,
         | though I did try.
        
       | potench wrote:
       | For others that, like me, do not know... a Mersenne prime is when
       | the n is prime and the resulting M is also prime in the following
       | equation.
       | 
       | M = 2n - 1
        
         | loup-vaillant wrote:
         | I didn't know, but according to Wikipedia we don't need to
         | require `n` to be prime, because when it isn't, then neither is
         | 2n-1. https://en.wikipedia.org/wiki/Mersenne_prime
         | 
         | So I prefer to shorten the definition to _" A prime of the form
         | 2n-1"_. It's bloody useful that n has to be prime though: makes
         | searching that much faster.
        
       | fnord77 wrote:
       | Still no Prime95 release build for Apple silicon
        
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