[HN Gopher] M(57885161) verified as 48th Mersenne Prime
___________________________________________________________________
M(57885161) verified as 48th Mersenne Prime
Author : mattashii
Score : 142 points
Date : 2021-10-10 09:26 UTC (13 hours ago)
(HTM) web link (www.mersenne.org)
(TXT) w3m dump (www.mersenne.org)
| hutrdvnj wrote:
| I think computer benchmarks should compute something useful, like
| mersenne prime verification. Million of benchmarks are run every
| day mostly on newer device with decent computing power. This
| amounts to a large amount of currently unused cycles.
|
| Maybe it would be possible to create a block-chain technology in
| which their participants calculate something scientifically
| meaningful.
| [deleted]
| david-gpu wrote:
| A benchmark must always perform the exact same computation for
| the same reason that all tape measures must be the exact same
| length.
| y7 wrote:
| You could run the exact same computation and still do
| something useful. The inputs do not have to be identical, but
| they can be coordinated (or random). Think of running a brute
| force search on some useful problem.
| jeroenhd wrote:
| Inputs definitely need to be identical because different
| inputs may lead to different behaviours in branch
| predictors and memory access patterns, affecting the score.
|
| The impact may be small, but I see no reason why the impact
| should be there in the first place just to satisfy some
| mathematicians' curiosity about special numbers.
| Jeff_Brown wrote:
| There are certain problems for which different inputs do
| not require different amounts of computer. "Add one to a
| number between 128 and 256" is an obvious example. The
| question is whether there are useful problems with that
| property.
| david-gpu wrote:
| Even a simple addition of two integers can take a
| different amount of energy to perform depending on the
| values involved. This in turn affects the temperature of
| the chip, which can cause thermal throttling. Computer
| architecture is more complex than most software engineers
| realize.
| jeroenhd wrote:
| Even such a task is subject to very specific
| requirements, because adding a number between 128 and 256
| may be enough to take another path in the microcode
| depending on if the result overflows or not. I'm not
| saying this happens kn practice, but I wouldn't be
| surprised if a future generation of processor would do
| this and make the entire benchmark invalid from that
| point on.
|
| A more likely scenario for such independent instructions
| would operate on an entire bit string, like boolean
| operators and vector instructions. I think you'd have a
| tough time producing any useful output from such an
| algorithm, though, because you wouldn't be able to do
| much with conditionals to keep the branch predictor score
| fair.
|
| I don't think that there are any algorithms that could
| operate within a generic benchmark that could have random
| elements in them _and_ product a useful result. Either
| the calculations are different and fair but meaningless,
| or they're exactly the same with the same result.
| Jeff_Brown wrote:
| Wow. That makes it sound like even a perfectly
| deterministic calculation cannot be compared across
| machines. Some will be good at some, some good at others,
| and whether one machine is overall better than another
| depends on their intended uses.
|
| Which now that I think about it, of course it would be
| like that. But still, what a headache for someone who
| just wants The Best One.
| dTal wrote:
| > I don't think that there are any algorithms that could
| operate within a generic benchmark that could have random
| elements in them _and_ product a useful result.
|
| One that springs to mind is Monte-Carlo sampled
| raytracing. An individual ray might take more or less
| time to compute, but the time to compute 10 million rays
| will be statistically be roughly constant. You could even
| imagine averaging a bunch of renders of the same scene
| from different machines to get a lower-noise result,
| thereby demonstrating a benchmark combined with useful
| work.
|
| Statistical predictability is the key.
|
| (Confession - this isn't exactly theoretical. I sometimes
| have occasion to render light fields, and I shard the
| work over as many random workstations as I can get my
| hands on. It's always obvious which workstations are
| faster than others, even without making any special
| attempt to balance the workload. I think this is actually
| a workable concept.)
| oasisbob wrote:
| > all tape measures must be the exact same length.
|
| Tape measures are useful even if they're not the same length.
|
| Higher-end engineering tapes acknowledge that length isn't
| constant, and provide temperature coefficients, ranges of
| accuracy, and tensioning guidelines.
|
| You can spend a lot of money on a tape measure which is more
| exact under more conditions. Most people don't need this.
| hutrdvnj wrote:
| Maybe it would be possible to design the scientifical
| computational tasks so that they are very similar in terms of
| stress for the CPU, but not completely even. You could then
| state that the benchmark offers comparable results with a
| statistical error of something like 2% +-0.5. You can also
| average the error by running the benchmark multiple times
| before you compare the score with other devices.
| kadoban wrote:
| By that point aren't you wasting as much computation time
| as you're trying to "save" by making it useful.
| hutrdvnj wrote:
| I don't think so, because every single
| benchmark/computation would be scientifically useful,
| even if you run it multiple times.
| jsnell wrote:
| Is Mersenne prime verification really scientifically
| useful? At this point, getting one more number verified
| seems about as useful as stamp collecting.
| hutrdvnj wrote:
| I don't see why we should be limited to Mersenne prime
| verification, there are many other scientific
| computational projects in various fields that could
| benefit from it, astrophysics, molecular biology,
| genetics, chemistry, climate study, cancer research, ...
|
| Wikipedia lists a few https://en.wikipedia.org/wiki/List_
| of_distributed_computing_...
| mattashii wrote:
| Mersenne prime verification is useful for the science
| field of mathematics, where the results can be used to
| (in)validate theories and predictions of (Mersenne) Prime
| Numbers. Sure, it is a niche with little contact area
| with the rest of thr world, but so were Elliptic Curves
| (used in cryptography), Set Theory and Relational Algebra
| (both heavily used in relational DB technology).
| foobarbecue wrote:
| There has been a lot of work on "proof of useful work" coins.
| https://gridcoin.us/ is the popular one. The benchmark idea
| doesn't work for the reasons other commenters raise.
| VMG wrote:
| This is a common misconception. In order for a Proof-of-Work
| algorithm to be useful, there must be an opportunity cost
| (penalty) to mining on the wrong chain. If the mining algorithm
| pays off anyway it cannot be used.
| yissp wrote:
| Unless the miners themselves benefit from the work, there
| would still be an opportunity cost to them, no? If it happens
| to be useful to someone else that shouldn't matter, right?
| garmaine wrote:
| If it is useful enough that someone is willing to pay for
| it as a service, then it fundamentally changes the
| incentive model and voids the security it provides.
| djbebs wrote:
| That matter because it gives those who it is useful an
| advantage in attacking the blockchain
| hutrdvnj wrote:
| The penalty is still there you pay the electric bill and it
| consumes time, but you would donate some cycles for useful
| scientific computational tasks without any benefit for
| yourself. If such an algorithm exist, then I don't see why
| this couldn't be used as Proof-of-Work algorithm.
| keymone wrote:
| PoW is a closed feedback loop system. Doing PoW yields you
| a reward, that reward pays for energy, that energy runs
| your PoW. If PoW yields you anything other in addition to
| normal reward - for you as a miner the only rational thing
| is to run more PoW with it to get more rewards. That in
| turn will simply bump the difficulty such that any
| additional benefit yielded will match the additional
| required energy expenditure to get the reward.
| lordnacho wrote:
| PoW works because showing a correctly mined block, ie one
| with a nonce that satisfies the many-initial-zeroes hash,
| proves that you on average (you can be short term lucky)
| have a used a certain amount of computing power.
|
| It proves it because with the selected algorithm, there's
| no known shortcut to just doing a load of hashes, so if you
| found one it means you did a lot of hashing.
|
| What problem would you insert instead that had the same
| properties?
|
| We should also not forget that it gets harder and harder
| for the same benefit. Any amount of energy can be poured
| into a PoW system. Invent fusion, use it all in crypto.
| needanon wrote:
| "Rent computational resource" could work with a
| verification of resource(s) step at the end of a set
| duration (block) and all of the computations performed
| using fully homomorphic encryption. If after the
| beginning of a block a random start time up to some max
| (~10 min) was selected for which the proving nodes would
| perform an operation to verify the resources were
| available and calculate the block hash instead of
| continuously burning, then at that starting time and for
| a set proving duration the verification algo would run
| and at the end the block would be distributed. Given the
| FHE was either running a paying program utilizing rented
| resources or the verification algo continuously, then it
| should not be possible to tell when the verification algo
| starts and stops. The non-FHE "gas" alternative that
| incentivizes performing program results to include in the
| hash has to have enough of an expected value that it
| would be prioritized over using the time to further
| calculate a minimal hash and the associated expected
| value for finding it without those gas incentivized
| transactions. The question is the FHE option more
| efficient than gas?
| lordnacho wrote:
| Is there a source of work that doesn't mind having its
| usage varied? And also will not be exhausted?
| [deleted]
| [deleted]
| fogof wrote:
| Whether or not there's an opportunity cost does matter, but
| why should this mean that the mining algorithm "paying off
| anyway" mean it can't be used? If the mining algorithm has an
| independent payoff whether or not you mine on the main chain,
| then there's still the same opportunity cost of the mining
| rewards.
| shakna wrote:
| One of the first I heard of was Primecoin [0], which still
| seems to be going along steadily. They've actually uncovered a
| number of world records [1] looking for Cunningham Chains.
|
| [0] https://primecoin.io/
|
| [1] https://primes.zone/#records
| toast0 wrote:
| Benchmarking really does need repeated inputs and outputs.
| Otherwise you can't make a meaningful comparison between the
| systems that ran the test.
|
| You can use these distributed computing projects for burn-in
| testing though. When you just want to run your computer hard to
| make sure it can manage N hours at 100%, and don't necessarily
| need to know how it compares to others, distributed computing
| can work (although, there's some risk of wrong results and
| therefore more work for the organizers if you're testing your
| system in extreme conditions, sometimes those lead to
| miscalculations)
| aaaaaaaaaaab wrote:
| How is Mersenne prime verification useful? It's in the same
| league as calculating pi to ever more enormous numbers of
| decimals...
| fsflover wrote:
| Both of which are useful for verifying mathematical
| predictions.
| gweinberg wrote:
| Like that the digits of pi look a lot like the output of a
| random number generator? I don't think that prediction is
| seriously in dispute.
| fsflover wrote:
| Yes, it is: https://en.wikipedia.org/wiki/Normal_number
| jameshart wrote:
| But generating yet more empirical data that it still
| seems pretty random out to digit _n_ does nothing to
| advance us to a proof that pi is normal.
| Zababa wrote:
| These are not unused cycles, these are cycles used to benchmark
| devices. If you benchmark with mersenne prime verification,
| you'll know how fast mersenne prime verification is and that's
| it. Most people don't use their devices for mersenne prime
| verification.
| gjhiggins wrote:
| In case it's of interest - Gapcoin's [1] Proof of Work function
| arguably does useful work by searching for large prime gaps of
| record merit ... "As of December 2017, the largest known merit
| value and first with merit over 40, as discovered by the
| Gapcoin network, is 41.93878373 with the 87-digit prime 2937032
| 340680225901587237661044194634257090755748117620985887982178957
| 28858676728143227. The prime gap between it and the next prime
| is 8350" [2] [1] https://gapcoin-project.github.io/ [2]
| https://en.wikipedia.org/wiki/Prime_gap
| ramshanker wrote:
| I imagine, one day when we finally break the factoring problem,
| we are going to have a bunch of these prime. This is one of the
| things I prat to see in my remaining lifetime.
| quantdev wrote:
| It's very possible we never break the factoring problem. Since
| we have no properly unified theory of physics (e.g., one that
| models the observer in QFT), there are outstanding unknowns
| with quantum computing that may make it so that Shor's
| algorithm is not practically useful.
| mseidl wrote:
| Crap, now I'm going to have to change the combination on my
| luggage.
| [deleted]
| devoutsalsa wrote:
| Imagine having 2^57885161 - 1 rollers on your luggage & having
| the lock bypassed by the low tech TSA key :)
| analog31 wrote:
| If its a binary lock, the combination was easy to guess.
| xyzelement wrote:
| I ask thos question with genuine curiosity- can someone help me
| understand why this is important? I have the same question about
| a lot of esoteric fields on Math - do we study them just because
| of curiosity and seeing how far we can follow a pattern? Or is
| there actual value to for example knowing what Mersenne primes
| are, etc?
|
| I guess my question is - is this applied in any way?
|
| EDIT: I see from responses my comment created the impression that
| I conflate "purely intellectual" and "not valuable." That was not
| my intention, simply asking whether this has applications or not.
| villasv wrote:
| > can someone help me understand why this is important
|
| Because it was hard
|
| > is this applied in any way
|
| Not sure, but this is a vacuous way to define what is important
| Ansil849 wrote:
| The only things "important" are having basic food to eat and a
| place to sleep. Everything else in life is "curiosity". It is
| incredibly annoying when the question of importance is brought
| up, typically when things like pure mathematics, or art, or
| humanities are being discussed. Why does no one ask, "can
| someone explain what's important about working for a FAANG
| company, what do they produce that's of any importance*.
| kibwen wrote:
| _> Why does no one ask, "can someone explain what's
| important about working for a FAANG company, what do they
| produce that's of any importance_.
|
| No, no, we ask that all the time. :P
| mike_d wrote:
| This is a _verification_ , the next likely Mersenne prime
| M(74207281) has already been discovered. Verification just
| involves eliminating all lower possibilities.
|
| https://www.mersenne.org/primes/
| karmakaze wrote:
| Thanks for this context. rank p
| digits discovered 48 257,885,161-1 17,425,170 2013
| Jan 25 49* 274,207,281-1 22,338,618 2016 Jan 07
| 50* 277,232,917-1 23,249,425 2017 Dec 26 51*
| 282,589,933-1 24,862,048 2018 Dec 07
|
| So we've already found three larger ones but have still yet to
| be verified as the 49th, 50th, 51st consecutive ones.
| Verification seem of more interest to those following closely
| and discovery of another one being bigger.
| Ansil849 wrote:
| I think one of the biggest mysteries (in my mind anyway), is how
| Mersenne found his original list of primes. Yes, some were shown
| to be incorrect and some he missed...but him finding the amount
| that he did still seems amazing to me, and I don't believe this
| has ever been explained.
|
| It seems to me like he had a private method for calculating
| primes (that was imperfect, sure, but also astounding for being
| developed in the 17th century).
|
| To me it feels like when this is brought up, modern day
| mathematicians are too quick to dismiss him based on the
| incorrect numbers/the missed primes, and ignore the many correct
| ones and the question of _how_ he managed to find them. That's
| what I would like to know, is his method.
| pvg wrote:
| _Yes, some were shown to be incorrect and some he missed_
|
| It's a small sample but it's worse than you make it sound, I
| think. He came up with four new numbers, given what was known
| at the time. _Half_ were wrong and he missed three. Whatever
| method he 'd come up with, it was pretty badly mistaken. It's
| curious, historically, but almost certainly mathematically
| uninteresting.
| Ansil849 wrote:
| > Whatever method he'd come up with, it was pretty badly
| mistaken. It's curious, historically, but almost certainly
| mathematically uninteresting.
|
| He did not just stumble onto two correct primes in the 17th
| century by chance. He had used a seemingly now-lost process
| that was semi-fruitful. This should be worthy of
| investigation, not dismissed as "mathematically
| uninteresting".
|
| Mersenne somehow figured out M(127)...in the early 1600s, and
| no one to this day seems to know how. How is this not
| mathematically interesting?
| pvg wrote:
| _He did not just stumble onto two correct primes in the
| 17th century by chance._
|
| M31 you can verify by hand, which really leaves us with one
| out of four. It's entirely possible he got one right by
| chance. It probably wasn't strictly by chance, very likely
| convinced himself of some pattern that doesn't really hold.
| There are plenty of neat-looking lines in, say, an Ulam
| spiral but those don't generate primes either.
| Archelaos wrote:
| Aprox. how much energy did this test consume?
| llampx wrote:
| Could someone tell me as a layperson, how finding these numbers
| is helping humanity?
| Ansil849 wrote:
| > Could someone tell me as a layperson, how finding these
| numbers is helping humanity?
|
| How do _you_ help humanity by browsing and posting? Like, what
| a weird thing to ask. I assume you ask the same thing of
| everything, right?
| inglor_cz wrote:
| "Helping humanity" is notoriously hard to measure, not least
| because people who are going to live in the 25th century are
| also part of "humanity" and yet we do not know how their world
| is going to look like.
|
| Mathematics in general is a bunch of stuff that often looks
| useless to laypeople or even professionals and may look so for
| 200 years until it very suddenly becomes relevant and crucial.
|
| The computer that you used to post your comment uses a lot of
| mathematical stuff developed in previous centuries. It is
| unlikely that Gauss or Euler could have predicted that their
| work (ink on paper) will one day be used to facilitate
| completely different modes of communication.
|
| And it is well possible that some priest criticized them for
| wasting their talents on abstract things that don't help
| humanity as of 1800.
| jameshart wrote:
| Sure, pure mathematical theory has a tendency to become
| useful later, but _finding specific Mersenne primes_ is not
| pure math.
|
| It's not known if there is an infinite number of Mersenne
| primes (though it is strongly suspected) - so an interesting
| mathematical object to discover would be 'the largest
| Mersenne prime' - but this process isn't going to find that
| (it might find a _candidate_ but it won't find a proof). If
| there are indeed infinite Mersennes then this search is just
| guaranteed to keep finding more forever.
|
| It's like looking for green pebbles on a beach. It's nice
| when you find one to add to your collection, but it's not
| that surprising, and if you keep looking you'll probably find
| more. You're not advancing geological knowledge if you keep
| looking and finding more.
| amonavis wrote:
| We don't know whether the search for further Mersenne
| primes eventually gives birth to a new algorithm which will
| enable further advances in other fields.
| jameshart wrote:
| Cranking on the current best known algorithm for testing
| for Mersenne primes does nothing to advance the state of
| the art for other algorithms, though.
|
| It's like saying, we have a project that keeps sorting
| larger and larger sets using quicksort because we believe
| it will help advance the state of sorting algorithms. 'We
| just sorted the largest ever set!'
| chx wrote:
| It can provide fuel for said algorithm.
| willis936 wrote:
| Yes but if you want to say if there are an infinite number
| of green pebbles on an infinitely large beach then the
| problem you need to solve is finding the distribution of
| the green pebbles on the beach. It's only possible to do
| that once you've found a few green pebbles and gets much
| easier if you've found many.
| Levitz wrote:
| I'm all for putting work to find things out and I agree with
| you, but for the sake of argument:
|
| Say these are really relevant 200 years down the line, maybe
| even 100 or 50, does it really make sense to calculate them
| now, given that computers 50, 100 and 200 years from now will
| outperform ours by orders of magnitude?
|
| Looking at this as reference:
| https://en.wikipedia.org/wiki/Microprocessor_chronology
|
| Say you grab a CPU from the end of the 70s and get it working
| until now, that'd be about 13*10e15 operations, or about a
| month of processing in a modern 5GHz CPU. That's 40 years to
| a month.
| inglor_cz wrote:
| Mathematics tends to be upstream of technology. I would
| expect that improvements in mathematical knowledge in
| general will _help us_ construct even better computers in
| the future. We are slowly approaching some physical limits,
| but algorithmic improvements may get us further speed
| improvements.
|
| IDK about this particular scientific team, but if you have
| to run a long-running task, you will be a lot more careful
| about complexity and speed of your data and algorithms
| instead of relying on brute force. Maybe you will actually
| discover some real improvements of existing knowledge.
|
| I can even see the effect throughout my IT life outside
| science. People who cut their teeth on processors with
| limited power and not enough RAM tend to produce much more
| efficient solutions even when programming modern computers.
| They just don't take the gigabytes and gigahertz for
| granted.
| limaoscarjuliet wrote:
| Yup. Math behind CT scan was developed in 1917. It was 50-ish
| years later it would be put to practical use.
| https://en.wikipedia.org/wiki/Radon_transform
| stathibus wrote:
| Apples and oranges. Naming more mersenne primes does not
| constitute discovering new mathematics. It's really very
| hard to argue that this is a good use of computing power.
| reikonomusha wrote:
| I think people will continue to search and observe things
| that they are unable to predict. This is true in almost
| any field.
| flafla2 wrote:
| Agreed with all of this, well put. I'd like to add though
| that we don't do math _just_ because we anticipate there will
| be some practical utility in a different field down the line.
| Mathematics isn't merely a prerequisite for engineering. Does
| it not suffice that we study math for the sake of it?
|
| The Mersenne primes for example are a delightful little
| mathematical object. IMO they are immediately curious and
| interesting. I am very grateful that we continue to make
| progress in understanding them.
| potiuper wrote:
| https://news.ycombinator.com/item?id=25308613
| q-big wrote:
| > Could someone tell me as a layperson, how finding these
| numbers is helping humanity?
|
| When people give such an argument, they usually mean "I am not
| interested in this topic" and use "why is this helping
| humanity" as an excuse for their ignorance.
| DoneWithAllThat wrote:
| I'd say it's worse, they're usually trying to imply that the
| people engaged in the activity aren't sufficiently allied
| with their pet political or moral causes. If you engage with
| their tweet-sized sniping the conversation inevitably leads
| to "why aren't they spending their time and resources
| addressing climate change/wealth inequality/poverty/etc."
| stathibus wrote:
| Such arrogance. It's funny that you mention climate change
| because this project is a non-negligible use of energy that
| is indefensible even in the context of advancing "pure
| mathematics." It's literally computation for the sake of
| computing more things that haven't been computed before.
| The only end result is that we can say we computed more
| things.
| DoneWithAllThat wrote:
| Case in point.
| opinion-is-bad wrote:
| I once had a math PhD friend tell me that if they ever became
| aware of any practical applications to their research, it would
| probably lose all interest to them. I've always found that to
| be curious and a good reminder that others can have radically
| different beliefs to my own in unexpected ways.
| sidpatil wrote:
| https://www.smbc-comics.com/comic/noooooooo
| ruuda wrote:
| https://abstrusegoose.com/504
| superjan wrote:
| RSA cryptography is is based on the assumption that factoring
| numbers is a hard problem. Isn't kind of nice to know that
| there curious people trying their best to see how fast you can
| actually get?
| AlexCoventry wrote:
| Primality tests for Mersenne numbers are highly specialized.
| It's possible that they could advance factorization of
| general numbers, but extremely unlikely.
| wmsiler wrote:
| I see this question getting downvoted, and some of the
| responses are strangely hostile strawman attacks based on what
| those posters are guessing this person "really" means. I think
| this is a perfectly reasonable question.
|
| A few years ago, I got a PhD in pure mathematics (low
| dimensional geometry and topology). As someone who loves pure
| math and spent many years devoted to it, I've had many
| conversations with mathematicians about whether we should be
| concerned with practical applications. One common argument,
| which several people have made here, is that there's been a lot
| of math that found practical application long after it was
| done. That really only applies to a very small proportion of
| math. The vast majority of math done has still never found
| application. So arguing that we should do that math because it
| may have applications later is kind of like arguing you should
| play the lottery since there's a greater than 0 chance that
| you'll win. Also, from the (admittedly biased) group of
| mathematicians I've spoken to about this, very few seemed to
| actually do math in the hope that it would be useful later.
|
| Instead, people do math because it's interesting, beautiful,
| and challenging. I would argue this Mersenne Prime search is
| almost more like recreation. I could be wrong, since I never
| did much number theory, but I don't think this is advancing any
| research. It's just a fun hobby for people who enjoy math. I
| think doing math for the sake of its beauty is generally fine.
| I do have concerns about the climate aspect of this particular
| project though. This is a lot of power being consumed just for
| recreation. This project may not be big enough to have much of
| an environmental impact, but in general, I think we should be
| more mindful of not wasting large amounts of computing power
| just for fun.
| jmopp wrote:
| The best example I can think of is GH Hardy's work on number
| theory. He was a pacifist and so specifically wanted to work on
| something that would not help the war effort. Fast forward 100
| years and number theory now forms the basis of modern
| cryptography - securing everything from your banking details to
| military communications.
|
| We often don't know what the applications are at the time, but
| that pure mathematics work very often forms the foundation of
| something important later on.
| m3kw9 wrote:
| He meant what is the practical use of this new discovery
| eloff wrote:
| This is hardly the most frivolous thing humanity does. It's ok
| if it never has any practical applications.
| ramraj07 wrote:
| On a different eon that might be true but nowadays compute
| power - electricity - global warming. Given that, "frivolous"
| work that just burns energy could be potentially postponed
| until we go fully renewable in our energy stack.
| f-jin wrote:
| You're in for a tough one once you find out that reality TV
| and video-games exist.
| mrpopo wrote:
| Or calculating SHA-256 hashes (ok this one already gets
| bashed out appropriately). Or running AC until you need a
| jacket.
| eesmith wrote:
| There seem to be many frivolous uses of power to complain
| about when you get to this level of power use.
|
| GIMPS' ~1PetaFLOPS[1] uses no more than a megawatt [2].
|
| That's about 10 Gigawatt-hours (GWh) over a year [3].
|
| The average US house uses about 10 MWh in a year [4] so
| GIMPS = the electrical power use of ~1,000 households.
| Portland reduced their power consumption by 20 GWh by
| switching their street lights to LEDs[5].
|
| The electrical consumption for Superbowl parties is an
| estimated 75 GWh [6]. (I think Superbowl parties are far
| more frivolous.)
|
| [1] - https://www.mersenne.org/primenet/
|
| [2] from 2012, "HP plans to deliver a full peak petaflop
| with just a single megawatt" - https://www.hpcwire.com/2012
| /09/05/hp_intel_score_petaflop_s...
|
| [3] 365.25days * 24hours/day * 1MW / 1000 = 8.8 GWh
|
| [4] "In 2020, the average annual electricity consumption
| for a U.S. residential utility customer was 10,715
| kilowatthours (kWh)"
| https://www.eia.gov/tools/faqs/faq.php?id=97&t=3
|
| [5] https://www.portlandoregon.gov/transportation/article/6
| 78781
|
| [6] https://www.americasgenerators.com/blog/post/2017/02/15
| /What...
| medo-bear wrote:
| lol ... bless you
| jacquesm wrote:
| The staying power of this project is very impressive, and the
| fact that even with the long interval between finds (years) that
| doesn't seem to detract from dedicating CPU power to the project.
|
| Carbon footprint anyone? ;)
| kevingadd wrote:
| If only we could use stuff like this or protein folding as the
| "work" in proof of work...
| koheripbal wrote:
| Primecoin
| tomerv wrote:
| That could really be a great thing! The problem is that
| Mersenne primes are "sparse", i.e. there aren't many of them.
| Finding one could be like minting a new block, but it would
| be so rare that it won't be practical. For crypto, you would
| need something with many solutions, but then it's probably
| not so useful to find yet another solution...
| the8472 wrote:
| maybe proof that a large block of numbers doesn't contain
| mersenne primes?
| dnautics wrote:
| you also generally speaking need something that is much
| easier to verify than it is to generate. I'm not saying it's
| impossible, but I don't think that "verifying" a protein
| folding in the "cryptocurrency" sense is a meaningful
| operation in the "useful" way you're hoping it to be.
| np_tedious wrote:
| Can you explain finding Mersenne primes so CPU intensive?
|
| M[?] = 2n - 1 gives an easy to generate candidate set and
| testing primality of a single number isn't _that_ expensive.
| 57885161th candidate being the 48th hit is getting pretty
| sparse I guess, but it isn 't that crazy. What am I missing?
| Seems the compute would be rather small compared to much of the
| "big data" / NN training done every day
| Someone wrote:
| Because they are so big. 103 > 1,000, so in decimal,
| 2^57,885,161 - 1 has over 3 x 5,788,516 digits, so over 17
| million.
|
| You do not check whether that is a prime by trial division
| (https://en.wikipedia.org/wiki/Trial_division). If you could
| do a division every nanosecond and had a billion devices,
| that would still take way, way more time than till the heat
| death of the universe to do.
|
| We have better tests (https://en.wikipedia.org/wiki/Primality
| _test#Fast_determinis...), but the best generic one still is
| O((log n)6). Here, log(n) is about 58 million, so that
| log(n)6 has over 46 digits.
|
| We can do better, as we don't need a generic test. for
| Mersenne numbers, there's
| https://en.wikipedia.org/wiki/Lucas-Lehmer_primality_test.
| jacquesm wrote:
| Because of the numers 'in between', once you start testing
| that many numbers in such an enormous range it eats up CPU
| power. There is some very beautiful math trickery which uses
| an FFT to help determine if a number is prime or not, and
| even though that's a massive optimization the number of
| remaining cycles required is still enormous.
|
| See here for more background:
|
| https://www.mersenne.org/various/math.php
| np_tedious wrote:
| Are Mersennes any more or less likely to be excluded by a
| probabilistic primality test than other numbers might be?
| pvg wrote:
| https://www.mersenne.org/various/math.php
|
| If you scroll to the very bottom there's some stuff on
| recent use of probable prime proofs, as well as a fairly
| detailed explanation of how the whole thing operates.
| cperciva wrote:
| The algorithm for testing a Mersenne number for primality
| has the same running time as performing a pseudoprime
| test, so there's no point using such probabilistic tests.
| It is however useful to perform "trial division" to
| exclude small factors.
| jacquesm wrote:
| I do not know. Maybe Colin Wright would be able to
| comment on this.
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