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### AuthorTopic: Random Stuff Part III  (Read 284605 times)

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#### liopoil

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##### Re: Random Stuff Part III
« Reply #2500 on: May 20, 2017, 02:01:49 pm »
0

34567876543 is a prime number!

I wonder if finding that by accident is sufficintly unlikely to warrant me feeling freaked out.

Also I noticed that every number the form 12321, 1234321 etc is exactly p^2*q^2 for two prime numbers p and q (and 121 is 11^2 and 1 is 1). I wonder why. I should really not spend time trying to figure it out.
It's not that unlikely. Almost 4% of numbers with 11 digits are prime, I estimate.

Well, 1 2 3 4 ...n-1 n n-1... 4 3 2 1 is equal to (10^n + 10^{n-1} + ... + 1000 + 100 + 10 + 1)^2. That is, 111...1 with n ones. When this number is the product of 2 primes, you're right. That's usually not the case though (first counterexample is 12345654321 I think).

EDIT: To say it precisely: ((10^{n+1} - 1)/9)^2 = (\sum_{k = 0}^n 10^k)^2 = \sum_{k = 0}^{2n} (n + 1 - |n - k|) 10^k
« Last Edit: May 20, 2017, 02:12:47 pm by liopoil »
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#### silverspawn

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##### Re: Random Stuff Part III
« Reply #2501 on: May 20, 2017, 02:20:22 pm »
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ew. I only tested towards 123454321 because the tool had a number cap.
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#### Titandrake

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##### Re: Random Stuff Part III
« Reply #2502 on: May 21, 2017, 02:18:05 am »
+3

More precisely, the 4% estimate comes from the prime number theorem, which says out of the numbers from 1 to n, about 1 / ln(n) of them will be prime.

This is actually pretty handy for cryptography, because some encryption algorithms rely on generating large random primes, and the prime number theorem guarantees you won't have to try too many random numbers to get there.
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#### Kirian

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##### Re: Random Stuff Part III
« Reply #2503 on: May 21, 2017, 02:44:52 am »
+2

ew. I only tested towards 123454321 because the tool had a number cap.

Well, 3 is prime.  And 5 is prime.  And 7 is prime.  Yep, every odd number greater than 1 is prime, that checks out!
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#### silverspawn

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##### Re: Random Stuff Part III
« Reply #2504 on: May 21, 2017, 02:50:46 am »
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ew. I only tested towards 123454321 because the tool had a number cap.

Well, 3 is prime.  And 5 is prime.  And 7 is prime.  Yep, every odd number greater than 1 is prime, that checks out!

But if the hypothesis is complex and every number has a tiny a priori chance of fulfilling it, I though I had great odds!
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#### Witherweaver

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##### Re: Random Stuff Part III
« Reply #2505 on: May 21, 2017, 09:33:01 am »
+4

There are some interesting examples of sequences that that do not fail to follow some apparently pattern until very large numbers (like in index at least of order 1e10).  They are apparently referred to as eventual counterexamples.

Polya conjecture is the one with the smallest counterexample around 1e10:
https://en.wikipedia.org/wiki/P%C3%B3lya_conjecture

https://math.stackexchange.com/questions/111440/examples-of-apparent-patterns-that-eventually-fail
https://mathoverflow.net/questions/15444/examples-of-eventual-counterexamples
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#### silverspawn

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##### Re: Random Stuff Part III
« Reply #2506 on: May 21, 2017, 10:02:49 am »
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That is really interesting.
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#### Awaclus

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##### Re: Random Stuff Part III
« Reply #2507 on: May 21, 2017, 10:12:05 am »
+3

Also I noticed that every number the form 12321, 1234321 etc is exactly p^2*q^2 for two prime numbers p and q (and 121 is 11^2 and 1 is 1). I wonder why. I should really not spend time trying to figure it out.

So I guess this was a real Parker Square of a pattern.
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#### Seprix

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##### Re: Random Stuff Part III
« Reply #2508 on: May 21, 2017, 04:25:59 pm »
+1

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#### Kuildeous

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##### Re: Random Stuff Part III
« Reply #2509 on: May 21, 2017, 11:44:48 pm »
+2

ew. I only tested towards 123454321 because the tool had a number cap.

Well, 3 is prime.  And 5 is prime.  And 7 is prime.  Yep, every odd number greater than 1 is prime, that checks out!

Nein!
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#### Tables

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##### Re: Random Stuff Part III
« Reply #2510 on: May 30, 2017, 03:31:19 pm »
+1

So I noticed this post from Coppernicus is getting a ton of upvotes this week: http://forum.dominionstrategy.com/index.php?topic=1276.msg20990#msg20990

I'm pretty confident the reason why is, well, he pretty much predicted a bunch of stuff from the newest expansions, several years before they came out. But how did a bunch of people notice that this week? Did someone point it out somewhere?
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...spin-offs are still better for all of the previously cited reasons.
But not strictly better, because the spinoff can have a different cost than the expansion.
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#### Mic Qsenoch

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##### Re: Random Stuff Part III
« Reply #2511 on: May 30, 2017, 03:41:10 pm »
+2

So I noticed this post from Coppernicus is getting a ton of upvotes this week: http://forum.dominionstrategy.com/index.php?topic=1276.msg20990#msg20990

I'm pretty confident the reason why is, well, he pretty much predicted a bunch of stuff from the newest expansions, several years before they came out. But how did a bunch of people notice that this week? Did someone point it out somewhere?

jsh pointed it out on the discord channel.
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#### pacovf

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##### Re: Random Stuff Part III
« Reply #2512 on: June 06, 2017, 01:15:29 am »
+1

Aaaaand Octopus Pie ended. Possibly the webcomic that had the most meaning for me and made me think the most.
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#### ashersky

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##### Re: Random Stuff Part III
« Reply #2513 on: June 06, 2017, 04:08:36 am »
0

For all of you Pokémon Go players out there...

http://www.ablogtowatch.com/romain-jerome-tourbillon-pokemon-watch/
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#### SpaceAnemone

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##### Re: Random Stuff Part III
« Reply #2514 on: June 06, 2017, 05:18:48 am »
0

For all of you Pokémon Go players out there...

http://www.ablogtowatch.com/romain-jerome-tourbillon-pokemon-watch/

I rather enjoy Pokémon Go, but ever since getting a smartphone, I've totally stopped wearing a watch.

I'm not sure I ever quite understood watch-as-a-personal/fashion-statement as opposed to watch-to-tell-the-time anyway.
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#### Awaclus

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##### Re: Random Stuff Part III
« Reply #2515 on: June 11, 2017, 03:03:18 pm »
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I have 3333 unread emails in my inbox.
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#### Tables

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##### Re: Random Stuff Part III
« Reply #2516 on: June 12, 2017, 04:04:53 pm »
+1

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...spin-offs are still better for all of the previously cited reasons.
But not strictly better, because the spinoff can have a different cost than the expansion.
I hereby declare myself the best dominion player in the world. Obviously.

#### Kirian

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##### Re: Random Stuff Part III
« Reply #2517 on: June 13, 2017, 02:57:03 pm »
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Ooooo... that's... actually a good idea.

My Inbox: 1955 unread out of 13085
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#### Kirian

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##### Re: Random Stuff Part III
« Reply #2518 on: June 13, 2017, 02:58:51 pm »
+2

Related:

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#### Awaclus

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##### Re: Random Stuff Part III
« Reply #2519 on: June 13, 2017, 03:06:58 pm »
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Ooooo... that's... actually a good idea.

My Inbox: 1955 unread out of 13085

I actually only have around 6025 emails total.
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#### silverspawn

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##### Re: Random Stuff Part III
« Reply #2520 on: June 13, 2017, 03:44:23 pm »
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I have no idea how you can do that. My observation is that ignoring mails for more than a few days is a really really bad idea that often gets me into trouble.

Unless you're talking about spam, of course.
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#### Awaclus

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##### Re: Random Stuff Part III
« Reply #2521 on: June 13, 2017, 03:47:08 pm »
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I have no idea how you can do that. My observation is that ignoring mails for more than a few days is a really really bad idea that often gets me into trouble.

Unless you're talking about spam, of course.

Not just spam but all sorts of notifications that I want to get but don't have to open, mostly.
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Bomb, Cannon, and many of the Gunpowder cards can strongly effect gameplay, particularly in a destructive way

#### silverspawn

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##### Re: Random Stuff Part III
« Reply #2522 on: June 13, 2017, 03:51:17 pm »
0

Oh, those mails don't go into the "unread" count for me. Bu yeah, those pile up quick.
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#### Tables

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##### Re: Random Stuff Part III
« Reply #2523 on: June 13, 2017, 03:56:41 pm »
+2

This is something I really like about Gmail. I get some notifications from advertisers and Twitch and stuff that all get automatically filtered out and don't go into my main inbox. Then when I have some spare time I give them a quick scan, see if anything is interesting that I care about, and hit mark all as read for the rest.
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...spin-offs are still better for all of the previously cited reasons.
But not strictly better, because the spinoff can have a different cost than the expansion.
I hereby declare myself the best dominion player in the world. Obviously.

#### Awaclus

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##### Re: Random Stuff Part III
« Reply #2524 on: June 13, 2017, 04:03:20 pm »
0

This is something I really like about Gmail. I get some notifications from advertisers and Twitch and stuff that all get automatically filtered out and don't go into my main inbox. Then when I have some spare time I give them a quick scan, see if anything is interesting that I care about, and hit mark all as read for the rest.

I get a lot of that stuff into my main inbox because I actually do want to notice it asap.
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Bomb, Cannon, and many of the Gunpowder cards can strongly effect gameplay, particularly in a destructive way