5 ms·

Why don't they say what it is?

CamperBob2 2y ago
Or even the number of digits.
lifthrasiir 2y ago
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.
- Dylan16807 2y ago
  It's hard to see how that someone would count as the discoverer.
  - lifthrasiir 2y ago
    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 probe the reports to find what it was anyway, but it is not easy to find one at least for me. If you are really looking for that, look for the P-PRP result type.) [1] https://www.eff.org/awards/coop/rules https://www.eff.org/awards/coop/rules
    - phkahler 2y ago
      Is there a probabilistic test for Mersene primes? I thought they just wanted confirmation via independent calculation.
      - lifthrasiir 2y ago
        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 https://www.mersenne.org/various/math.php#prp
      - deleted 2y ago
        [deleted]
      - af3d 2y ago
        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!).
  - Jerrrrrrry 2y ago
    How hard? NP hard? I wonder why? :)
- schoen 2y ago
  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_perfect_numbers 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.
  - lifthrasiir 2y ago
    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 ;-)
    - schoen 2y ago
      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.
- gus_massa 2y ago
  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.
  - ColinWright 2y ago
    There are primality proving certificates. https://en.wikipedia.org/wiki/Primality_certificate 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.

Or even the number of digits.

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.

Dylan16807 2y ago
It's hard to see how that someone would count as the discoverer.
- lifthrasiir 2y ago
  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 probe the reports to find what it was anyway, but it is not easy to find one at least for me. If you are really looking for that, look for the P-PRP result type.) [1] https://www.eff.org/awards/coop/rules https://www.eff.org/awards/coop/rules
  - phkahler 2y ago
    Is there a probabilistic test for Mersene primes? I thought they just wanted confirmation via independent calculation.
    - lifthrasiir 2y ago
      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 https://www.mersenne.org/various/math.php#prp
    - deleted 2y ago
      [deleted]
    - af3d 2y ago
      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!).
- Jerrrrrrry 2y ago
  How hard? NP hard? I wonder why? :)
schoen 2y ago
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_perfect_numbers 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.
- lifthrasiir 2y ago
  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 ;-)
  - schoen 2y ago
    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.
gus_massa 2y ago
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.
- ColinWright 2y ago
  There are primality proving certificates. https://en.wikipedia.org/wiki/Primality_certificate 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.