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New Mersenne Prime discovered (probably)

mersenne.org

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Re: New Mersenne Prime discovered (probably)

#121

Post by ahazred8ta »

tirant wrote: post #64
zeven7 wrote: post #46

Earlier quoted context omitted.

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!

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…

Maxim 19: The world is richer when you turn enemies into friends, but that's not the same as you being richer.

Re: New Mersenne Prime discovered (probably)

#122

Post by af3d »

Jerrrrrrry wrote: post #101
poincaredisk wrote: post #94

Earlier quoted context omitted.

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'

Yes, the Mersenne primes do indeed extend to infinity. That is due to the simple fact that perfect numbers (for which they are intimately connected to) are also known to be infinite in number.

Re: New Mersenne Prime discovered (probably)

#123

Post by af3d »

phkahler wrote: post #18
lifthrasiir wrote: post #13

Earlier quoted context omitted.

That someone will totally count as the discoverer under the current rules [1], because it requires the deterministic primality proof for given number. It doesn't matter how much effort was taken to reach that candidate so far, even though it would be virtually impossible to find any new prime without that. I think the temporary embargo is fully justified for this reason. (And I think it is technically possible to pro…

Is there a probabilistic test for Mersene primes? I thought they just wanted confirmation via independent calculation.

It's called the "Lucas–Lehmer primality test". Without it, GIMPS probably wouldn't have found a single one of them in an acceptable amount of time. The one that was just discovered is HUGE. I had to write a program just to slow down the output enough to be able to appreciate its shear magnitude (it is still printing as I write this!).

Re: New Mersenne Prime discovered (probably)

#124

Post by schoen »

lifthrasiir wrote: post #28
schoen wrote: post #26

Earlier quoted context omitted.

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…

M43112609 (2008-08) was discovered prior to M42643801 (2009-06), so that order is not really strict. I agree that there is a human tendency to test smaller primes (thus faster to verify) first, but it should be also noted that every single Mersenne number smaller than M124399361 has been already tested at least once by someone even though that limit would be way higher than what we have for primes. There are also som…

They've now published the prime, and it's turned out to be somewhere in between our speculations (new exponent 1.65× the length of the previous exponent discovery).

https://www.mersenne.org/primes/?press=M136279841

Re: New Mersenne Prime discovered (probably)

#125

Post by Jerrrrrrry »

af3d wrote: post #122
Jerrrrrrry wrote: post #101

Earlier quoted context omitted.

Should be able to trivially extend that logic to Mersenne Primes then, 'presumably'

Yes, the Mersenne primes do indeed extend to infinity. That is due to the simple fact that perfect numbers (for which they are intimately connected to) are also known to be infinite in number.

This was an instant deduction, thank you.

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.

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