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New Mersenne Prime discovered (probably)

mersenne.org

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Re: New Mersenne Prime discovered (probably)

#81

Post by mort96 »

ISL wrote: post #50
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.

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?

Re: New Mersenne Prime discovered (probably)

#82

Post by mort96 »

stevefan1999 wrote: post #60
aaronmdjones wrote: post #58

Earlier quoted context omitted.

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).

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

And we look for Mersenne primes, AFAIU, mainly because Mersenne numbers are more likely to be prime than other numbers, so it's easier to find big primes that way.

Re: New Mersenne Prime discovered (probably)

#83

Post by fhars »

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").

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

Re: New Mersenne Prime discovered (probably)

#84

Post by fhars »

schoen wrote: post #57
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?

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…

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?

Re: New Mersenne Prime discovered (probably)

#85

Post by lagadu »

mort96 wrote: post #81
ISL wrote: post #50

Earlier quoted context omitted.

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.

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?

I'm not an SME but I would imagine that if there's some sort of very large scale pattern in Mersenne primes then finding that might lead to the discovery of some currently unknown emergent property. Of course this argument is likely unfalsifiable, as it can scale infinitely if there's an infinite amount of them, though we don't even know whether they are a finite set or not.

Re: New Mersenne Prime discovered (probably)

#86

Post by tomtomtom777 »

mort96 wrote: post #81
ISL wrote: post #50

Earlier quoted context omitted.

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.

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?

Isn't the fact that a certain number is a Mersenne prime interesting in itself? Surely it's a great addition to our knowledge of numbers?

Re: New Mersenne Prime discovered (probably)

#87

Post by stavros »

Aurornis wrote: post #43
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.

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

Re: New Mersenne Prime discovered (probably)

#88

Post by stavros »

rollinDyno wrote: post #35
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.

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.

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.

Re: New Mersenne Prime discovered (probably)

#89

Post by Waterluvian »

fhars wrote: post #83
schoen wrote: post #27

Earlier quoted context omitted.

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").

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

It’s not quite 137, though. The last digit needs to be oh so slightly off.

Re: New Mersenne Prime discovered (probably)

#90

Post by School-Cotton »

aaronmdjones wrote: post #58
stevefan1999 wrote: post #56

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?

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).

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