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New Mersenne Prime discovered (probably)

mersenne.org

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Re: New Mersenne Prime discovered (probably)

#41

Post by aphantastic »

Jerrrrrrry wrote: post #39
freeqaz wrote: post #36

Earlier quoted context omitted.

Is there a good POW mechanism that would test primes? I found this but curious what else exists! https://en.wikipedia.org/wiki/Primecoin

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 transi…

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?)

Re: New Mersenne Prime discovered (probably)

#42

Post by Jerrrrrrry »

schoen wrote: post #26
lifthrasiir wrote: post #24

Earlier quoted context omitted.

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 ;-)

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 5× as large rather than something like 1.05× as large as the previous r…

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.

Re: New Mersenne Prime discovered (probably)

#43

Post by Aurornis »

ziofill wrote: post #3

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.

> 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.

Re: New Mersenne Prime discovered (probably)

#45

Post by m463 »

schoen wrote: post #27
MPSimmons wrote: post #10

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

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").

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)

Re: New Mersenne Prime discovered (probably)

#46

Post by zeven7 »

Jerrrrrrry wrote: post #34
aphantastic wrote: post #32

Earlier quoted context omitted.

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?

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.

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!

Re: New Mersenne Prime discovered (probably)

#47

Post by Jerrrrrrry »

aphantastic wrote: post #41
Jerrrrrrry wrote: post #39

Earlier quoted context omitted.

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 transi…

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?)

  >(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

Re: New Mersenne Prime discovered (probably)

#50

Post by ISL »

dataflow wrote: post #48

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?

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.

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