Dominion Strategy Forum

Please login or register.

Login with username, password and session length
Pages: 1 ... 99 100 [101] 102 103 ... 123  All

Author Topic: Random Stuff Part III  (Read 242159 times)

0 Members and 1 Guest are viewing this topic.

liopoil

  • Margrave
  • *****
  • Offline Offline
  • Posts: 2587
  • Respect: +2475
    • View Profile
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 »
Logged

silverspawn

  • Governor
  • *****
  • Offline Offline
  • Posts: 4093
  • Shuffle iT Username: sty.silver
  • ♦ Twilight ♦
  • Respect: +1814
    • View Profile
Re: Random Stuff Part III
« Reply #2501 on: May 20, 2017, 02:20:22 pm »
0

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

Titandrake

  • Mountebank
  • *****
  • Offline Offline
  • Posts: 2069
  • Respect: +2499
    • View Profile
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.
Logged
I have a blog! It's called Sorta Insightful. Check it out?

Kirian

  • Adventurer
  • ******
  • Offline Offline
  • Posts: 7088
  • Shuffle iT Username: Kirian
  • An Unbalanced Equation
  • Respect: +9342
    • View Profile
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!
Logged
Kirian's Law of f.DS jokes:  Any sufficiently unexplained joke is indistinguishable from serious conversation.

silverspawn

  • Governor
  • *****
  • Offline Offline
  • Posts: 4093
  • Shuffle iT Username: sty.silver
  • ♦ Twilight ♦
  • Respect: +1814
    • View Profile
Re: Random Stuff Part III
« Reply #2504 on: May 21, 2017, 02:50:46 am »
0

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!
Logged

Witherweaver

  • Adventurer
  • ******
  • Offline Offline
  • Posts: 6460
  • Shuffle iT Username: Witherweaver
  • Respect: +7817
    • View Profile
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

Some other links:

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

silverspawn

  • Governor
  • *****
  • Offline Offline
  • Posts: 4093
  • Shuffle iT Username: sty.silver
  • ♦ Twilight ♦
  • Respect: +1814
    • View Profile
Re: Random Stuff Part III
« Reply #2506 on: May 21, 2017, 10:02:49 am »
0

That is really interesting.
Logged

Awaclus

  • Adventurer
  • ******
  • Offline Offline
  • Posts: 10875
  • Shuffle iT Username: Awaclus
  • (´。• ω •。`)
  • Respect: +11481
    • View Profile
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.
Logged
Bomb, Cannon, and many of the Gunpowder cards can strongly effect gameplay, particularly in a destructive way

The Twitch channel where I stream DominionThe YouTube channel where I make musicDownload my band's albums for free

Seprix

  • Adventurer
  • ******
  • Offline Offline
  • Posts: 5534
  • Shuffle iT Username: Seprix
  • Respect: +3480
    • View Profile
    • The Border Village
Re: Random Stuff Part III
« Reply #2508 on: May 21, 2017, 04:25:59 pm »
+1

Logged
Don't let this one slip, or you could be going to military school.

Join Dominion Discord

Kuildeous

  • Cartographer
  • *****
  • Online Online
  • Posts: 3733
  • Respect: +2141
    • View Profile
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!
Logged
A man has no signature

Tables

  • Margrave
  • *****
  • Offline Offline
  • Posts: 2735
  • Build more Bridges in the King's Court!
  • Respect: +3223
    • View Profile
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?
Logged
...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.

Mic Qsenoch

  • 2015 DS Champion
  • *
  • Offline Offline
  • Posts: 1670
  • Respect: +4249
    • View Profile
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.
Logged

pacovf

  • Cartographer
  • *****
  • Offline Offline
  • Posts: 3358
  • Multiediting poster
  • Respect: +3695
    • View Profile
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.
Logged
pacovf has a neopets account.  It has 999 hours logged.  All his neopets are named "Jessica".  I guess that must be his ex.

ashersky

  • Mountebank
  • *****
  • Offline Offline
  • Posts: 2336
  • 2013/2014/2015 Mafia Mod of the Year
  • Respect: +1509
    • View Profile
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/
Logged
f.ds Mafia Board Moderator

2013, 2014, 2015 Mafia Mod of the Year

Games (30): Mafia: 17, 21, 24, 31, 39, 43, 67, 72, 86 || Newbie: 7 || RMM: 6, 7, 10, 20, 22, 26, 32, 45 || Blitz: 4-7, X, 17-19, 22, 24 || BM: 14, 19

2015 f.ds Representative, World Forum Mafia Championships
2013, 2014 Mafia Player of the Year (Tie)

Town: 47 Games, 24 Wins
Scum: 22 Games, 13 Wins
11x MVP: M30, M83, ZM16, M25, M38, M61, M76, RMM5, RMM41, RMM46, M51

SpaceAnemone

  • Spy
  • ****
  • Offline Offline
  • Posts: 86
  • Shuffle iT Username: SpaceAnemone
  • Correct Horse Battery Staple
  • Respect: +26
    • View Profile
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.
Logged
Congratulations! Your SpaceAnemone evolved into UniverseAnemone!
Town games: M84(L), M85(W), M86(L), M87(W), M88(L), M90(L), M92(W), M94(L), M97(L), M99(W), M100(L), M104(W), M107(W), M110(L), M112(L), RMM37(L), RMM40(D), RMM41(L), RMM43(L), RMM47(W), ZM23(W).
Scum games: M89(D), M108(L), NM8(W&MVP), NM10(L)   Mod: NM9, RMM38, RMM42.   Pronouns: they/them

Awaclus

  • Adventurer
  • ******
  • Offline Offline
  • Posts: 10875
  • Shuffle iT Username: Awaclus
  • (´。• ω •。`)
  • Respect: +11481
    • View Profile
Re: Random Stuff Part III
« Reply #2515 on: June 11, 2017, 03:03:18 pm »
0

I have 3333 unread emails in my inbox.
Logged
Bomb, Cannon, and many of the Gunpowder cards can strongly effect gameplay, particularly in a destructive way

The Twitch channel where I stream DominionThe YouTube channel where I make musicDownload my band's albums for free

Tables

  • Margrave
  • *****
  • Offline Offline
  • Posts: 2735
  • Build more Bridges in the King's Court!
  • Respect: +3223
    • View Profile
Re: Random Stuff Part III
« Reply #2516 on: June 12, 2017, 04:04:53 pm »
+1

I very rarely go above about 10 unread emails. I read the bits I actually care about, then hit mark all as read for the rest.
Logged
...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

  • Adventurer
  • ******
  • Offline Offline
  • Posts: 7088
  • Shuffle iT Username: Kirian
  • An Unbalanced Equation
  • Respect: +9342
    • View Profile
Re: Random Stuff Part III
« Reply #2517 on: June 13, 2017, 02:57:03 pm »
0

I very rarely go above about 10 unread emails. I read the bits I actually care about, then hit mark all as read for the rest.

Ooooo... that's... actually a good idea.

My Inbox: 1955 unread out of 13085
Logged
Kirian's Law of f.DS jokes:  Any sufficiently unexplained joke is indistinguishable from serious conversation.

Kirian

  • Adventurer
  • ******
  • Offline Offline
  • Posts: 7088
  • Shuffle iT Username: Kirian
  • An Unbalanced Equation
  • Respect: +9342
    • View Profile
Re: Random Stuff Part III
« Reply #2518 on: June 13, 2017, 02:58:51 pm »
+2

Related:

Logged
Kirian's Law of f.DS jokes:  Any sufficiently unexplained joke is indistinguishable from serious conversation.

Awaclus

  • Adventurer
  • ******
  • Offline Offline
  • Posts: 10875
  • Shuffle iT Username: Awaclus
  • (´。• ω •。`)
  • Respect: +11481
    • View Profile
Re: Random Stuff Part III
« Reply #2519 on: June 13, 2017, 03:06:58 pm »
0

I very rarely go above about 10 unread emails. I read the bits I actually care about, then hit mark all as read for the rest.

Ooooo... that's... actually a good idea.

My Inbox: 1955 unread out of 13085

I actually only have around 6025 emails total.
Logged
Bomb, Cannon, and many of the Gunpowder cards can strongly effect gameplay, particularly in a destructive way

The Twitch channel where I stream DominionThe YouTube channel where I make musicDownload my band's albums for free

silverspawn

  • Governor
  • *****
  • Offline Offline
  • Posts: 4093
  • Shuffle iT Username: sty.silver
  • ♦ Twilight ♦
  • Respect: +1814
    • View Profile
Re: Random Stuff Part III
« Reply #2520 on: June 13, 2017, 03:44:23 pm »
0

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.
Logged

Awaclus

  • Adventurer
  • ******
  • Offline Offline
  • Posts: 10875
  • Shuffle iT Username: Awaclus
  • (´。• ω •。`)
  • Respect: +11481
    • View Profile
Re: Random Stuff Part III
« Reply #2521 on: June 13, 2017, 03:47:08 pm »
0

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.
Logged
Bomb, Cannon, and many of the Gunpowder cards can strongly effect gameplay, particularly in a destructive way

The Twitch channel where I stream DominionThe YouTube channel where I make musicDownload my band's albums for free

silverspawn

  • Governor
  • *****
  • Offline Offline
  • Posts: 4093
  • Shuffle iT Username: sty.silver
  • ♦ Twilight ♦
  • Respect: +1814
    • View Profile
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.
Logged

Tables

  • Margrave
  • *****
  • Offline Offline
  • Posts: 2735
  • Build more Bridges in the King's Court!
  • Respect: +3223
    • View Profile
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.
Logged
...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

  • Adventurer
  • ******
  • Offline Offline
  • Posts: 10875
  • Shuffle iT Username: Awaclus
  • (´。• ω •。`)
  • Respect: +11481
    • View Profile
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.
Logged
Bomb, Cannon, and many of the Gunpowder cards can strongly effect gameplay, particularly in a destructive way

The Twitch channel where I stream DominionThe YouTube channel where I make musicDownload my band's albums for free
Pages: 1 ... 99 100 [101] 102 103 ... 123  All
 

Page created in 0.236 seconds with 21 queries.