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GIMPS Project Discovers Largest Known Prime Number

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Re: GIMPS Project Discovers Largest Known Prime Number

#41

Post by dghughes »

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 will only emerge at the same time every 220 years (I think it as).

Smart bugs!

Re: GIMPS Project Discovers Largest Known Prime Number

#42

Post by xamuel »

schoen wrote: post #25
kryptiskt wrote: post #18

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.

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 mankind [ideally eventually] knows the primality of all primes.

Contrast: Which Turing machines will mankind [ideally eventually] know are never-halting? This is a much harder question and the answer is probably not "all never-halting Turing machines"

Re: GIMPS Project Discovers Largest Known Prime Number

#43

Post by sidhack »

dghughes wrote: post #41

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…

Is this the 3-part BBC documentary - "The Code"?

Re: GIMPS Project Discovers Largest Known Prime Number

#44

Post by schoen »

xamuel wrote: post #42
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.

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

Re: GIMPS Project Discovers Largest Known Prime Number

#46

Post by sillysaurus3 »

lettergram wrote: post #31
imhelpingu wrote: post #6

So that's what it's working on when it's starting up.

I know typically jokes like this aren't HN material, but have an up vote lol Literally, the first thing I though of was GIMP as well :)

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.

Re: GIMPS Project Discovers Largest Known Prime Number

#48

Post by vlunkr »

lettergram wrote: post #31
imhelpingu wrote: post #6

So that's what it's working on when it's starting up.

I know typically jokes like this aren't HN material, but have an up vote lol Literally, the first thing I though of was GIMP as well :)

It seems to me that jokes are ok, just not spamming the same old jokes, as you might on Reddit.

Re: GIMPS Project Discovers Largest Known Prime Number

#49

Post by WhitneyLand »

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

Re: GIMPS Project Discovers Largest Known Prime Number

#50

Post by lettergram »

sillysaurus3 wrote: post #46
lettergram wrote: post #31

Earlier quoted context omitted.

I know typically jokes like this aren't HN material, but have an up vote lol Literally, the first thing I though of was GIMP as well :)

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.
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