

Prime Gap Grows After Decades-Long Lull - digital55
https://www.quantamagazine.org/20141210-prime-gap-grows-after-decades-long-lull/

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typomatic
I laughed out loud when I saw that formula--y = loglogloglog x is a nonsense
function. For those of you who haven't thought about logs for a while, that
function is increasing (bigger x give bigger y), but it grows so slowly that y
won't be larger than 1 until x is larger than 2.33 x 10^1656520.

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prezjordan
Is loglogloglog...log the only beast that can conquer Knuth's arrow notation?
(x ↑↑↑↑...↑ n)

Every time I watch videos about arrow notation or, more famously, Graham's
number, my head explodes :)
[https://www.youtube.com/watch?v=GuigptwlVHo](https://www.youtube.com/watch?v=GuigptwlVHo)

Big big numbers are really, really cool!

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anonetal
log*(x) = how many times you have to take a log before you get to 1, grows
more slowly than any constant length sequence of logs, and also appears
naturally in many theoretical algorithms (e.g., union-find). I suspect even
that is not enough to tame Knuth's arrow notation though.

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jordigh
Union-find's big-Oh is the inverse of the Ackermann function, which isn't
quite the same as iterated logs...

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charrison
Depends on how you derive it. I've seen derivations that end up with a log*
term. Of course, inverse Ackermann is a tighter bound.

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lkbm
> This is the first Erdös prize problem Tao has been able to solve, he said.
> “So that’s kind of cool.”

There are only fifteen, right? Possibly even fewer open ones. It'd be pretty
impressive if he/they manage to solve multiple Erdös prize problems.

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ggchappell
You might be thinking of something else. Erdős was constantly remarking that
he would offer some amount for some problem. I would guess there are hundreds
of open problems with Erdős prizes attached -- some large, some small.

I can't find a list. Odd.

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chx
[http://mathoverflow.net/questions/27716/does-there-exist-
a-c...](http://mathoverflow.net/questions/27716/does-there-exist-a-
comprehensive-compilation-of-erdoss-open-problems)

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darkstar999
What is the significance of studying this problem? I mean, say they prove the
twin primes conjecture. What does that mean? Do we benefit like we would if
the travelling salesman problem was solved?

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StefanKarpinski
This is a different but related problem: instead of trying to prove that there
are arbitrarily large twin primes, they are trying to see how the maximum gap
between primes grows with their size. I know that doesn't answer the
applicability question, but I think the answer to that is "who knows?" Pure
mathematicians tend to study these things for their own sake and then someone
may or may not figure out something useful to do with it.

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Florin_Andrei
Conjecture: Given enough time for science to make progress, eventually all
mathematical theorems and conjectures will gain applicability in practice.

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WhitneyLand
The weaker claim that at least some findings will gain applicability in
practice should be well enough to justify all of our efforts.

