New Mersenne Prime discovered (probably)
mersenne.org
mersenne.org
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.
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. :-)
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.
I found this but curious what else exists! https://en.wikipedia.org/wiki/Primecoin
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.
>(for instance what happens when you prove a prior established complexity wrong?)
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.
10 years!
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.
Primemarkcoin
Perceptiongapcoin
Liecoin
epiplexiscoin
and of course, the every useful pyramidcoin and scamcoin.
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.
> 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).
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.
But nope, it's just a similar acronym! https://en.wikipedia.org/wiki/Great_Internet_Mersenne_Prime_...
https://www.schneierfacts.com/facts/365
from the "Bruce Schneier Facts" series (which was inspired by the "Chuck Norris Facts").
(it's like a prime protected carry-on that schneier carries)
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.
It’s the longest wait for a new mersenne prime since the discovery of M32 in 1992.
How about something like Superoptimizing (with correctness proofs) open source code?
Perhaps there is a pattern or a way to more-accurately predict which numbers will be prime.
Also, it is cool.
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
>presumably go on infinitely long
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.
I tried some flavors of primes but you'd think the most intuitive one by a magnitude would be listed on the Wiki for proofs.
>I didn't claim there are an infinite number of Mersenne primes.
you actually almost got me :)
"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."
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.
(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.)
NP hard?
I wonder why?
:)
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.
But yeah, they'd probably embargoed even without any potential monetary prizes because it's wise to do so in general ;-)
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.
[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!
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.
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.
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.
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”
I think you may be wrong by at least 3 orders of magnitude.
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.
M = 2ⁿ - 1
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.
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