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Math

51st Known Mersenne Prime Number Found (mersenne.org) 65

Posted by EditorDavid from the prime-of-your-life dept.
chalsall (Slashdot reader #185), writes: The Great Internet Mersenne Prime Search (GIMPS) has discovered the largest known prime number, 2^82,589,933-1, having 24,862,048 digits. A computer volunteered by Patrick Laroche from Ocala, Florida made the find on December 7, 2018.

GIMPS has been on amazing lucky streak, finding triple the expected number of new Mersenne primes -- a dozen in the last fifteen years.
"This anomaly is not necessarily evidence that existing theories on the distribution of Mersenne primes is incorrect," notes GIMPS. "However, if the trend continues it may be worth further investigation. " They also report that the newly-discovered prime number "is more than one and a half million digits larger than the previous record prime number" -- and it's one of just 51 known Mersenne prime numbers ever discovered. "GIMPS, founded in 1996, has discovered the last 17..."

Patrick Laroche is one of thousands of volunteers using GIMPS' free software to hunt for prime numbers -- and is now eligible for a $3,000 "research discovery award," the group writes at mersenne.org. "GIMPS' next major goal is to win the $150,000 award administered by the Electronic Frontier Foundation offered for finding a 100 million digit prime number" -- of which $50,000 will be awarded to the discoverer, with another $50,000 going to a 501(c)(3) mathematics-related charity selected by GIMPS, and $50,000 retained by GIMPS to cover expenses and fund other awards.
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51st Known Mersenne Prime Number Found More

51st Known Mersenne Prime Number Found

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  • Prime numbers (Score:5, Funny)

    by Hognoxious ( 631665 ) on Saturday December 22, 2018 @07:47PM (#57847138) Homepage Journal

    A prime number can only be divided by one, itself, and Chuck Norris.

  • Might want to look for a bug in your code first, before going on to blame mathematical theory.

  • Cool (Score:1)

    by ch-chuck ( 9622 )

    Thanks - I can use that as one of the primes in my 82 billion bit private key - lets see the NSA crack that!

    • Re: (Score:1)

      by ch-chuck ( 9622 )

      Believe it or not, the free Mathematica on a Raspberry Pi can calculate p = 2^82589933 - the last line is (without the -1)

        > 6640076912114355308311969487633766457823695074037951210325217902592

      Right now it's counting the digits (and may run out of memory yet)

      In[2]:= Total[DigitCount[p]]

      nope, just got the answer:
      Out[2]= 24862048

    • Thanks - I can use that as one of the primes in my 82 billion bit private key - lets see the NSA crack that!

      They will have no problem cracking that at all, because that prime number will be _known_.

  • No use for for cryptography but still interesting (Score:5, Informative)

    by JoshuaZ ( 1134087 ) on Saturday December 22, 2018 @08:46PM (#57847310) Homepage

    And before anyone asks, no these large Mersenne are much too large to be used in practical cryptography. There is a random number generator called a Mersenne twister which does use a Mersenne prime, but that uses much smaller ones to be feasible, and in any event is not sufficiently random to be safe for serious cryptographic purposes.

    The primary interest in these primes is two-fold: First they have a very efficient primality test, the Lucas-Lehmer test https://en.wikipedia.org/wiki/Lucas-Lehmer_primality_test [wikipedia.org] and so if one is interested in simply finding very big primes, these are the ones to look for. For most of the last 100 years the largest known prime has beena Mersenne prime.

    Second, there's a connection with perfect numbers. A number is said to be perfect if the sum of all its positive divisors which are less than the number add up to the number. For example, 6 is perfect because 1,2 and 3 divide 6 and 1+2+3=6. But 8 is not perfect because 1+2+4=7 which is not perfect. The two oldest unsolved problems in all of math are a) are there any odd numbers which are perfect and b) are there infinitely many even numbers which are perfect? About 2000 years ago, Euclid recorded a proof (which may or may not have been due to him) that every Mersenne prime allows you to construct an even perfect number. In the 1700s, Euler proved that any even perfect number must arise from Euler's construction. So if one cares about answering this question about even perfect numbers, then one wants to investigate Mersenne primes.

    • Re:No use for for cryptography but still interesti (Score:4, Insightful)

      by Kjella ( 173770 ) on Saturday December 22, 2018 @09:31PM (#57847464) Homepage

      About 2000 years ago, Euclid recorded a proof (which may or may not have been due to him) that every Mersenne prime allows you to construct an even perfect number.

      I "rediscovered" that proof as a teenager, and thought I was breaking new ground. Then I found it was actually discovered 2000+ years ago. Mathematics has a special way of putting your hubris in perspective.

      • I "rediscovered" that proof as a teenager, ... Then I found it was actually discovered 2000+ years ago.

        But did Euclid bother to register it with the corresponding Copyright/Patent Offices? No? Then IT'S STILL UP FOR GRABS, DO IT NOW. Add "ON A COMPUTER" and you're golden.

        Or just say you identify as Euclid today and don't even bother. It didn't work for this guy [telegraph.co.uk] but he was arguing about age, which is math. And we all know that "Math Is Hard" from that great sage: Barbie.

      • About 2000 years ago, Euclid recorded a proof (which may or may not have been due to him) that every Mersenne prime allows you to construct an even perfect number.

        I "rediscovered" that proof as a teenager, and thought I was breaking new ground. Then I found it was actually discovered 2000+ years ago. Mathematics has a special way of putting your hubris in perspective.

        No need for the scare quotes. If you found it on your own then you legitimately rediscovered it.

    • What is practical application of this if not for cryptography

    • Print it out [youtube.com] and you could use it as a paper weight. Or just talk about it for a while [youtube.com] I guess.

    • I did a ballpark estimate of the odds of finding a new Mersenne prime. It's very roughly 1 in 100,000 that an untested number that has no small factors (less than 2^76) will be prime.

      Just one Mersenne prime has been found between 2^44 million and 2^74 million, and then there are no less than 3 in the next 10 million powers of 2 (minus 1 of course)? That's a lot.

      It adds to our knowledge. Maybe we can see more patterns, or figure out something else interesting. The more data we have...

  • Did they use a computer for that?
  • With the price of crypto-currencies on what looks like a downward trend, this past week being an exception, could all that GPU and crypto-mining HW be put to use fishing for gimps?

    • Yes. The most effective GIMPS use of GPUs is currently trial factoring. That is basically brute force division of the candidate number by small factors, which can eliminate candidates faster than doing a full Lucas-Lehmer [wikipedia.org] or probable primality [wikipedia.org] test. The new prime was trial factored by numbers up to 75 bits long. The optimal bit depth to trial factor to depends on the GPU hardware, especially the double-precision to single-precision ratio. Trial factoring can leverage SP, while the current LL and PRP impleme

      • Most of that is way over my head. I have always assumed that prime number searching would use integer math, think that was faster and that floating point would have rounding errors.

  • Wait, so the GIMP photo editor all along was just a ploy to search for Prime Numbers !?

  • Why the EFF? (Score:4, Interesting)

    by mentil ( 1748130 ) on Sunday December 23, 2018 @03:49AM (#57848432)

    "GIMPS' next major goal is to win the $150,000 award administered by the Electronic Frontier Foundation offered for finding a 100 million digit prime number"

    Wait a minute, why is a civil liberties group funding a contest to solve mathematical problems? Following the link, they make it pretty clear that their ordinary funding doesn't go toward this, and apparently one interested party gave them the funds for this specific purpose. Still doesn't answer why they approached the EFF instead of, say, CERN.

    • Prime numbers are essential to modern cryptography, so it makes sense for the EFF to fund research into primes. While the newest Mersenne primes aren't readily necessary for cryptography, there's a lot more to the research. For instance, someone might discover a better way of predicting the distribution of prime numbers, which would make prime-based encryption weaker.

      • Prime numbers are essential to modern cryptography

        Not really. Prime numbers and the ability to generate them quickly and the difficulty of factoring products of large primes are essential to RSA, but that's on its way out anyway (too slow, too easy to implement incorrectly). Primes are relevant to ECC, but less so. Some ECC curves are in prime fields, others are not -- and the prime values used are all published, so prime distribution doesn't matter. The next, post-quantum, generation of asymmetric cipher and key agreement algorithms may or may not make u

    • i suspect that the real answer to this involves John Perry Barlow getting really high with Whitfield Diffie once.

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