Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

GIMPS Project Discovers Largest Known Prime Number

mersenne.org

Post reply on HN
Print view View original

81–90 of 115 posts

Re: GIMPS Project Discovers Largest Known Prime Number

#81

Post by qmalzp »

chimeracoder wrote: post #72
netcraft wrote: post #15

so I didn't know this, but got curious about how many known prime there are - I knew there were infinite primes, but thought that there would be some concrete list of all the primes that we had discovered somewhere - but apparently not https://math.stackexchange.com/questions/272791/how-many-pri... > Nobody's really keeping count. ... There are very many hundred-digit primes to find. We could cover the Earth in hardd…

> so I didn't know this, but got curious about how many known prime there are This isn't the exact question you're asking, but we actually know the distribution of prime numbers, which allows us to calculate the (approximate) number of primes that are less than or equal to an arbitrary value. Since the largest prime discovered is 2^(277,232,917-1), that means that the number of primes less than or equal to that numbe…

Nit: the largest prime discovered is

2^(277,232,917)-1

not

2^(277,232,917-1)

Re: GIMPS Project Discovers Largest Known Prime Number

#84

Post by voltagex_ »

sillysaurus3 wrote: post #58
lettergram wrote: post #50

Earlier quoted context omitted.

Reading over that, I actually recognize I miss the older HN - where the conversations seemed fairly long and in depth. It's still often the case, but it does seem like the average length and depth is decreasing.

I completely agree. There are a few contributing factors, none of which are unsolvable. But it seems like the way to solve it is to essentially fork HN. The current plan is to create a "mirror" of HN's front page, but with a smaller community. You'll be bale to keep your HN name, because you won't be allowed to use someone's existing HN name on the new site unless you claim it. Then, we'll need content. This was the…

What did the mod team do to you? This is the second time I've seen you have a go at them today.

Re: GIMPS Project Discovers Largest Known Prime Number

#85

Post by schoen »

sowbug wrote: post #71
schoen wrote: post #25

Earlier quoted context omitted.

Interestingly, those primes' primality is normally proven statistically rather than deductively. This is not really a practical issue for people using RSA, but could be a philosophical issue for someone interested in the question of how many different numbers' primality has been proven by humanity.

Not that I worry about this much, but if the fast prime generation methods we use are imperfect, then how bad is it when someone's PGP key or TLS certificate is based on nonprimes? Do black-hats ever strike gold and find out that someone's key is easily factorable? Or is there an additional property of common primality tests that their errors tend to be insignificant? (e.g., yes, this number isn't really prime, but i…

I think there was some research about this that did find some flawed implementations leading to semiprime p or q, but basically you can choose the probability that a probable prime is actually composite to be low enough that the expected number of weak keys ever generated for this reason is still less than one.

(I haven't personally understood the probabilistic primality tests well enough to understand how they guarantee that the probability of error contributed by each round of the test is completely independent of every other round.)

Re: GIMPS Project Discovers Largest Known Prime Number

#86

Post by fooker »

schoen wrote: post #44
xamuel wrote: post #42

Earlier quoted context omitted.

When philosophers study mankind's knowledge, it's more typical to study the things mankind would ideally know at the end of all time assuming mankind could continue forever. (Formally: the knowledge predicate is usually assumed to satisfy modus ponens: if mankind knows "A implies B" and mankind knows "A", then mankind knows "B") Under this abstraction, if mankind knows the axioms of logic and Peano arithmetic, then m…

It's a little funny that mankind gets to use a full-fledged infinite-tape Turing machine in order to compute arbitrarily large computations, since no such machine would fit in our universe. https://en.wikipedia.org/wiki/Limits_of_computation https://en.wikipedia.org/wiki/Transcomputational_problem

The description of a Turing machine that can do arbitrarily large computations can be finite. See: Kolmogorov complexity.

Re: GIMPS Project Discovers Largest Known Prime Number

#88

Post by tribby »

sohkamyung wrote: post #87

Curious: can bitcoin mining rigs be modified for BOINC projects (GIMPS, Seti@Home, etc.)? If yes, than I might invest in some rigs and modify them to run BOINC. Yes, I'm weird: I prefer to do computation for BOINC than for bitcoin. :-)

nowadays bitcoin mining rigs use ASICs that are optimized for the task, so I don't think that would be a good idea.

on a general purpose system you can use GPUs and BOINC with SETI, not sure about GIMPS.

Re: GIMPS Project Discovers Largest Known Prime Number

#89

Post by yarg »

WhitneyLand wrote: post #49

But why? One answer is a bit buried in a sub link in the article. On that page, you’ll find arguments for the following reasons: tradition, by products of the quest, collection of rare mathematical things, glory, pushing hardware performance, and contest rewards. Personally I’m forced to admit I enjoy seeing them found while being unable to form any cogent justification. http://primes.utm.edu/notes/faq/why.html

They're a nice source of mathematically justifiable entropy.

Re: GIMPS Project Discovers Largest Known Prime Number

#90

Post by schoen »

fooker wrote: post #86
schoen wrote: post #44

Earlier quoted context omitted.

It's a little funny that mankind gets to use a full-fledged infinite-tape Turing machine in order to compute arbitrarily large computations, since no such machine would fit in our universe. https://en.wikipedia.org/wiki/Limits_of_computation https://en.wikipedia.org/wiki/Transcomputational_problem

The description of a Turing machine that can do arbitrarily large computations can be finite. See: Kolmogorov complexity.

Sure, but it feels a little funny in one way to say that people "know" all of its output, although I'd agree that for other purposes being able to write a program to generate something is a relatively good description of what it means to understand it.
Post reply on HN