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>presumably go on infinitely long prove it
It's well established that there are infinite prime numbers, for example https://www-users.york.ac.uk/~ss44/cyc/p/primeprf.htm
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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 hav…
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.
lol, like the government doesn't have 3 more Mersennes they keep secret so they can verify potential First Contact situations
They're much easier to verify than to find. Just ask for the next one hundred unknown primes and check the response.
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.
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 peop…
I think you may be wrong by at least 3 orders of magnitude.
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?
>presumably go on infinitely long prove it
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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.
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.
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.
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 peop…
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.
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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.
Is there a good POW mechanism that would test primes? I found this but curious what else exists! https://en.wikipedia.org/wiki/Primecoin
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.
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It's well established that there are infinite prime numbers, for example https://www-users.york.ac.uk/~ss44/cyc/p/primeprf.htm
Should be able to trivially extend that logic to Mersenne Primes then, 'presumably'
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.