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GIMPS Project Discovers Largest Known Prime Number

mersenne.org

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Re: GIMPS Project Discovers Largest Known Prime Number

#51
post #45
post #38

Earlier quoted context omitted.

For producing something of no intrinsic monetary value?

How are these any different from say Bitcoin?

Bitcoin doesn't pay out cash when you find a block. It pays out Bitcoins. So the value of that is based on how much other people will pay for a bitcoin.

Re: GIMPS Project Discovers Largest Known Prime Number

#52

Earlier quoted context omitted.

Mm, if something is subtly funny, it's usually welcome. One of my favorite jokes of all time was pg's nickb april fools prank: https://news.ycombinator.com/item?id=151109#152361 Probably worth putting together a list of HN moments... There were so many.

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.

"Nostalgia was better in the old days" ~ unknown author

Re: GIMPS Project Discovers Largest Known Prime Number

#54
post #37
post #7

> Jonathan Pace is a 51-year old Electrical Engineer living in Germantown, Tennessee. Perseverance has finally paid off for Jon - he has been hunting for big primes with GIMPS for over 14 years. What a great story.

I know he's a volunteer but only $3000? Does that seem low to anyone else?

I don't think anyone is doing this to make a quick buck, just for fun.

Re: GIMPS Project Discovers Largest Known Prime Number

#55
post #25

Earlier quoted context omitted.

RSA encryption keys uses the product of two large primes, where each prime is many digits long. So many new primes are "discovered" every day.

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.

RSA implementations do use probabilistic primality tests when generating primes. OpenSSL [0] uses the Miller-Rabin primality test for RSA, which can be wrong, but they use enough iterations to make it very unlikely.

[0]: https://wiki.openssl.org/index.php/Manual:BN_generate_prime(...

Re: GIMPS Project Discovers Largest Known Prime Number

#56

Prime numbers are amazing. I was watching a math documentary and one example was a Cicada in North Carolina that only emerges once every thirteen years millions of them at once. It's a defense mechanism the sheer number overwhelms predators. The Cicada does this also to avoid appearing when another species of Cicada appears to prevent cross breeding. The other species in the same region emerges every 7 years. The two…

I vaguely remember watching the same documentary, so I don't doubt you. But surely they would emerge at the same time every 21 years?

Edit: I looked it up, its 13 and 17 years, giving a 221 year overall cycle. I guess it only really "matters" that the years are coprime.

https://en.wikipedia.org/wiki/Periodical_cicadas

Re: GIMPS Project Discovers Largest Known Prime Number

#57
post #44
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

[deleted]

Re: GIMPS Project Discovers Largest Known Prime Number

#58

Earlier quoted context omitted.

Mm, if something is subtly funny, it's usually welcome. One of my favorite jokes of all time was pg's nickb april fools prank: https://news.ycombinator.com/item?id=151109#152361 Probably worth putting together a list of HN moments... There were so many.

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 secret sauce in the early HN days. The sole reason for people to come to the new site would be good conversation, and I think recruiting a few of the writers from HN would be enough to bootstrap it. Part of HN's early success was that pg actually participated in HN. Whereas the current mod team just shows up to beat us over the head and little else.

If you want to help plan this out, contact me (email's in profile). I think we have a shot at this. Some past thoughts on the topic:

https://news.ycombinator.com/item?id=16064078

https://news.ycombinator.com/item?id=16044466

Getting away from the heavy-handed moderation will be the best part. Comments will be free to flow into tangents, as long as they're substantive.

Re: GIMPS Project Discovers Largest Known Prime Number

#59
post #29
post #12

Earlier quoted context omitted.

> Mersennes are beautiful and have some surprising applications. Unfortunately that page doesn’t elaborate on what these surprising applications are, which is itself surprising on a page that purports to answer “why”.

It automatically results in the discovery of a new perfect number. :-) https://en.wikipedia.org/wiki/Euclid%E2%80%93Euler_theorem (combining two of history's greatest mathematicians with names that have confused generations of students by being pronounced very differently)

Euler and Gauss are (for now, at least) in my opinion the greatest mathematicians of the past two millenia (1000-1999, 2000-). Al-Khawarizmi takes the cake for the millennium before that. Then it's Euclid all the way back ;)
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