New Mersenne Prime discovered (probably)

https://www.mersenne.org/

by sdsykes • 2 years ago

368 120 2 years ago

mersenne.org

jmclnx• 2 years ago

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• 2 years ago

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.

lifthrasiir6• 2 years ago

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• 2 years ago

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• 2 years ago

I've seen that movie too

Nition• 2 years ago

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• 2 years ago

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.

schoen7• 2 years ago

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. :-)

aphantastic2• 2 years ago

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?

fuglede_• 2 years ago

I'm curious how this is organized.

because GIMPS always at least eventually gives out numbers to multiple people to check

For the 40th Mersenne prime, 2²⁰⁹⁹⁶⁰¹¹ − 1, for example, the status page on mersenne.org seems to suggest only a single check (and a handful of later NF checks later), but maybe follow-up proofs and proof certifications and reruns are omitted? https://www.mersenne.org/report_exponent/?exp_lo=20996011&fu...

Also, when you sign up, you're asked to provide an email address in case they want to get in touch with you, so even if OP didn't themselves do so, I imagine they would include their work just the same?

However, your name could have ended up on that Wikipedia list as a discoverer. :-)

Along the same lines, since each (potential) prime is being worked on by many computers, some looking for factors, some running the Fermat test, some running proof certification work, who gets the "discoverer" title; just the person who ran the PRP test? If so, seems fair enough, since that's where most of the computational budget ends up, but on the other hand, it seems like that would disincentivize running anything but PRP tests. But maybe the people involved are just in it for the mission (or the GHz day leaderboards).

rollinDyno• 2 years ago

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.

Jerrrrrrry13• 2 years ago

its like "the game" but you feel like you got stabbed by Hindsight herself

stavros2• 2 years ago

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• 2 years ago

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.

stavros2• 2 years ago

Does it take months to check one prime? Maybe the author got extremely lucky.

solardev• 2 years ago

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• 2 years ago

I absolutely had the same thought progression

beyondCritics• 2 years ago

Great news for humanity.

hyperhello• 2 years ago

We get free two-day shipping on our Mersennes.

xanderlewis• 2 years ago

Thanks, Jeff!

dooglius• 2 years ago

Why don't they say what it is?

CamperBob2• 2 years ago

Or even the number of digits.

lifthrasiir6• 2 years ago

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• 2 years ago

It's hard to see how that someone would count as the discoverer.

schoen7• 2 years ago

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.

gus_massa• 2 years ago

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.

MPSimmons• 2 years ago

Time for Bruce Schneier to change the combination to his luggage again

schoen7• 2 years ago

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• 2 years ago

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• 2 years ago

thank you for the education :) this is so good!

fhars2• 2 years ago

Not 137? https://www.schneier.com/blog/archives/2005/06/picking_physi...

hinkley• 2 years ago

Luggage that would make Dan Brown green with envy.

throwawee• 2 years ago

Needlessly confusing if Dan Brown is green and Dan Green is white. Somebody standardize Dans.

natas• 2 years ago

Chuck Norris has already discovered and factorized all the prime numbers.

toast0• 2 years ago

A number is prime if its factors are itself, one, and Chuck Norris.

dudeinjapan2• 2 years ago

A number is prime if it is the number of times Chuck Norris roundhouse kicked Optimus Prime

ramshanker• 2 years ago

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• 2 years ago

y-cruncher is the king of stress testing

dudeinjapan2• 2 years ago

Hell yeah!! This is the best thing to happen all week!!!

Eliezer• 2 years ago

lol, like the government doesn't have 3 more Mersennes they keep secret so they can verify potential First Contact situations

Jerrrrrrry13• 2 years ago

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• 2 years ago

They're much easier to verify than to find. Just ask for the next one hundred unknown primes and check the response.

Jerrrrrrry13• 2 years ago

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.

dataflow3• 2 years ago

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• 2 years ago

It’s exploration of new lands

ISL• 2 years ago

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.

mort963• 2 years ago

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?

schoen7• 2 years ago

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/

fhars2• 2 years ago

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?

Jerrrrrrry13• 2 years ago

  >presumably go on infinitely long

prove it

poincaredisk• 2 years ago

It's well established that there are infinite prime numbers, for example https://www-users.york.ac.uk/~ss44/cyc/p/primeprf.htm

dataflow3• 2 years ago

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.

benreesman• 2 years ago

I turned 40 recently and it was the only devastating milestone before or since. No excuses: I blew that.

jl6• 2 years ago

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• 2 years ago

amazing how many bitcoins have been discovered since then. Satoshi should've incentivized mining something useful.

yreg• 2 years ago

Are these high Mersenne primes all that useful?

iamgopal• 2 years ago

every new prime for new block, but not linear.

stevefan19992• 2 years ago

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• 2 years ago

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).

stevefan19992• 2 years ago

Oh, right, all Mersenne number is in the form of 2^N -1, but Mersenne prime is Mersenne number plus being prime

umanwizard• 2 years ago

A lot simpler example is 2^4-1=5*3

Jabrov• 2 years ago

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• 2 years ago

https://oeis.org/A000043

sfelicio• 2 years ago

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• 2 years ago

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• 2 years ago

https://github.com/preda/gpuowl

p5a0u9l• 2 years ago

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• 2 years ago

“$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• 2 years ago

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• 2 years ago

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-vaillant2• 2 years ago

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• 2 years ago

Still no Prime95 release build for Apple silicon

gcanyon• 2 years ago

Anyone have a sense of how much money/electrical power is being spent to discover these primes? I'm not about to argue for bitcoin calculations over this, I'm just curious how it compares.

New Mersenne Prime discovered (probably)

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