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New Mersenne Prime discovered (probably)

mersenne.org

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Re: New Mersenne Prime discovered (probably)

#21

Post by schoen »

lifthrasiir wrote: post #9
dooglius wrote: post #7

Why don't they say what it is?

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.

I used to run the Cooperative Computing Awards, and I don't think this is the reason in this case.

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.

Re: New Mersenne Prime discovered (probably)

#22

Post by lifthrasiir »

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.

Any probabilistic primality test will work, but GIMPS currently uses the first-time Fermat probable prime test with a very robust certificate [1] to filter almost all non-primes in advance.

[1] https://www.mersenne.org/various/math.php#prp

Re: New Mersenne Prime discovered (probably)

#23

Post by schoen »

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.

If it was literally around "20+ years ago", like 2004 or slightly before, it might have been M40 or M41.

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. :-)

Re: New Mersenne Prime discovered (probably)

#24

Post by lifthrasiir »

schoen wrote: post #21
lifthrasiir wrote: post #9

Earlier quoted context omitted.

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.

I used to run the Cooperative Computing Awards, and I don't think this is the reason in this case. 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_Mersenn…

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 ;-)

Re: New Mersenne Prime discovered (probably)

#25

Post by Jerrrry »

therein wrote: post #19
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'd believe it. Many years ago when I was around 10 years old and not understanding the concept of probability properly, I decided I had come up with a way to enumerate the lottery numbers and come up with a reasonably sized set of numbers to place bets for. I proceeded to write 9 pages of numbers for my father to place bets for. It is a 6/49 lottery so 6 balls are drawn from a set of 49 and you need to get all of th…

I've seen that movie too

Re: New Mersenne Prime discovered (probably)

#26

Post by schoen »

lifthrasiir wrote: post #24
schoen wrote: post #21

Earlier quoted context omitted.

I used to run the Cooperative Computing Awards, and I don't think this is the reason in this case. 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_Mersenn…

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 record.

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.

Re: New Mersenne Prime discovered (probably)

#27

Post by schoen »

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").

Re: New Mersenne Prime discovered (probably)

#28

Post by lifthrasiir »

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…

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 some groups of people that specifically look for prime numbers that are barely enough to be 100,000,000+ decimal digits [1]. Given we didn't see any new Mersenne prime for many years, new prime from a random range seems much more likely than ever.

[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!

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