[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
___________________________________________________________________
(page generated 2024-10-19 23:01 UTC)