0247: "Factoring the Time"
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Delurking to say that this is what I do instead of counting sheep. It works if I'm trying to get to sleep between 10:00 and 12:59 (my clock is set to 12hour time).
Tricks for "is X factorable by P" are all based off modulo arithmetic. I find the breakingtheunitsdigitoff tricks most accessible while lying awake at night. They are all of the form,
"XXXXU is divisible by P iff XXXX + F_P * U is divisible by P."
F_7 is 2, so 1453 is divisible by 7 iff (145  2*3 = 139) is.
For twodigit primes, applying this trick to P itself lets you figure out F_P pretty quickly; usually quickly enough to then use the trick and factor the time in under a minute. You need to regenerate P or some multiple of it:
13: 1+4*3=13, so F_13 = 4
17: 15*7 = 34; F_17 = 5
19: 1+2*9 = 19; F_19 = 2
similarly, F_23 = 7, F_29 = 3, F_31 = 3, F_37 = 11, and so on
Tricks for "is X factorable by P" are all based off modulo arithmetic. I find the breakingtheunitsdigitoff tricks most accessible while lying awake at night. They are all of the form,
"XXXXU is divisible by P iff XXXX + F_P * U is divisible by P."
F_7 is 2, so 1453 is divisible by 7 iff (145  2*3 = 139) is.
For twodigit primes, applying this trick to P itself lets you figure out F_P pretty quickly; usually quickly enough to then use the trick and factor the time in under a minute. You need to regenerate P or some multiple of it:
13: 1+4*3=13, so F_13 = 4
17: 15*7 = 34; F_17 = 5
19: 1+2*9 = 19; F_19 = 2
similarly, F_23 = 7, F_29 = 3, F_31 = 3, F_37 = 11, and so on
I actually got bored enough to code this one up:
/* This code will take every number that can be displayed
on a 24hour digital clock and find its prime factors. Output
to file recommended.
Implementation of void factor(int) left as an
exercise & to keep from spamming the board. */
/* This code will take every number that can be displayed
on a 24hour digital clock and find its prime factors. Output
to file recommended.
Implementation of void factor(int) left as an
exercise & to keep from spamming the board. */
Code: Select all
int main(int argc, char *argv[])
{
int x = 0;
for (x; x != 2401; ++x){
if (x%100 == 60) {
x += 40;
}
printf("%d:%02d ", x/100, x%100) ;
factor(x);
}
return 0;
}
For whom it might interest (as if you couldn't do it yourself , my Mathematica line for finding the prime times:
Select[Select[Range@2359, Mod[#, 100] < 60 &], PrimeQ]
Or if you wish to factor all valid times:
FactorInteger /@ Select[Range@2359, Mod[#, 100] < 60 &]
This is for people like me who can't do arithmetic in their head but want to feel nerdy anyway.
Select[Select[Range@2359, Mod[#, 100] < 60 &], PrimeQ]
Or if you wish to factor all valid times:
FactorInteger /@ Select[Range@2359, Mod[#, 100] < 60 &]
This is for people like me who can't do arithmetic in their head but want to feel nerdy anyway.
Splarka wrote:After that, this was naturally called for: factor clock javascript (see if you can do it faster)
And of course factor clock extreme! (can you still do it faster? haha)
Bugger, you beat me to it:
Tom's factor clock
My code's cleaner, than yours, though! And it might even be faster, depending on how javascript implements array extension ...
 tom
My own factor clock. I wrote it earlier, before I thought to check the forums. Anywho, it has a few options and I think it displays more nicely than the others (but of course I'm biased).
It is nicer.Anywho, it has a few options and I think it displays more nicely than the others (but of course I'm biased).
[edit]What's the largest number of factors that a time can have? What if you allow seconds as well?
I mostly post over at LessWrong now.
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I've been counting the number of footsteps between different places on campus lately. If had a stopwatch, I'd be timing the walks, dividing by the number of steps, finding the average for a series of tests, and using that to determine exactly how fast I can get from place to place, so that I can consistently only be two minutes late instead of five.
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Aaron Haynes wrote:I've been counting the number of footsteps between different places on campus lately. If had a stopwatch, I'd be timing the walks, dividing by the number of steps, finding the average for a series of tests, and using that to determine exactly how fast I can get from place to place, so that I can consistently only be two minutes late instead of five.
No, if you had a stopwatch, you'd use it to to figure out when to leave so that you could get places on time. Because that's what watches are for. Also what time is for.
Sorry, but I really dislike lateness, both in myself and others. Most of the time I would rather not show up to something than to show up late. And there are few things more annoying than some jackass wandering in late to class and knocking over everyone's desks while they walk all the way to the back.
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nikolasco wrote:My own factor clock. I wrote it earlier, before I thought to check the forums. Anywho, it has a few options and I think it displays more nicely than the others (but of course I'm biased).
Hehe, I just stumbled upon that. Wanted to see if you reported it yet.

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Our maths teacher would never let the class start untill we had found some patern in the date, I haded 2006 because there weren't any prime number days (23/7/05 for example) and she always got excetiedn and ina very good mood on such days, to the extent of geting maried on one (23/7/05 if memory serves).
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I once wrote a C program which determined (a) whether my phone number is prime, and if it is, (b) which prime it is. It took a couple hours to write, and about 20 minutes on my 1.8GHz laptop to finish. It turns out that my phone number is the 338,319,598th prime. Sw33t.
[EDIT]: Ladies, call me? :P
[EDIT]: Ladies, call me? :P
Last edited by gnutun on Sun Apr 15, 2007 11:29 pm UTC, edited 1 time in total.

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I like to do the four 4's game.
You take four 4's and can use any operation (or common function or uncommon function, whatever) to try and get whatever number.
i.e.
0 = 44  44
1 = 44/44
2 = 4/4 + 4/4
3 = (4+4+4)/4
4 = sqrt(4) + sqrt(4)  4 + 4
5 = sqrt(4) + sqrt(4) + 4/4
6 = (4!/4)  4 + 4
7 = 4 + (4!/4)/sqrt(4)
8 = 4 + 4 + 4  4
9 = 4 + 4 + 4/4
10 = 4 + 4 + 4  sqrt(4)
etc.
You take four 4's and can use any operation (or common function or uncommon function, whatever) to try and get whatever number.
i.e.
0 = 44  44
1 = 44/44
2 = 4/4 + 4/4
3 = (4+4+4)/4
4 = sqrt(4) + sqrt(4)  4 + 4
5 = sqrt(4) + sqrt(4) + 4/4
6 = (4!/4)  4 + 4
7 = 4 + (4!/4)/sqrt(4)
8 = 4 + 4 + 4  4
9 = 4 + 4 + 4/4
10 = 4 + 4 + 4  sqrt(4)
etc.
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themuffinking wrote:I like to do the four 4's game.
You take four 4's and can use any operation (or common function or uncommon function, whatever) to try and get whatever number.
<examples>
Any uncommon function, you say?
So let's say I wanted to find a way to make the number 1337. I could say, okay, let's have f(x) = 1337. So then we can use four 4's and get: f(4444)=1337. Win?
Iluvatar wrote:Love: Gimme the frickin' API.
yy2bggggs, on Fischer Random chess wrote:Hmmm.... I wonder how how a hypermodern approach would work
I'd say, looking at the rules of that game, that you'd need to define the function as part of the thingy, and you're only allowed four 4s still. So you could have f(x)=4x+4, f(4)/4, but not f(x)=3, f(4444), because that's using a digit other than 4.
Surely it is as ridiculous to consider sqrt(1) "imaginary" because you can't use it to count pieces of chalk as to consider the number 200 imaginary because by itself it cannot express the location of one point with reference to another. Isaac Asimov

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nikolasco wrote:My own factor clock. I wrote it earlier, before I thought to check the forums. Anywho, it has a few options and I think it displays more nicely than the others (but of course I'm biased).
Your clock is better. Of course, it has to be. If you posted it after and it was worse, it'd be a huge letdown.
One thing though  the whole reason I found this forum was to complain that the comic treated the time as a decimal number instead of sexagesimal. I like that you have that option on there, however you only go halfway. You treat the time as sexagesimal, but not the factors. That's why I had to go and register...
I think the point is: you can't (or rather shouldn't, for some value of "should") factor time as decimal because it's not a number in a vacuum. It has units. When you multiply 23 x 11 and get 253, if you want to express that as a time, it's 253 seconds, which is 4:13. Conversely, when you factor 4:13 into prime factors, you shouldn't be factoring it into numbers in a vacuum but into other times, i.e. 00:23 x 00:11. Which I would assume is fine if you just render it as 23 x 11.
But when you factor, say, 23:21, it shouldn't render as 11 x 211, it should be 11 x 3:31. Where 3:31 is a prime time. Or even 00:11 x 3:31. I don't know, I think I just like the aesthetics of showing a clock time as a product of other times, specifically as a product of prime times. It's got kind of a cyclical quality to it.
Of course, don't think that the point is lost on me, here. I know the sheer worthlessness of factoring into primes, and more so the inanity of arguing over how to do it and how to render the results, but, you know, what the hey...
Oh, and incidentally... you know what would be the sweetest thing? If your factor clock actually had the output fields inside the comic... assuming that wouldn't be infringement.

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I was bored and coded it in perl... and then had the incredible urge to obfuscate it, so i did just that.
the number it factors is the number that's given as the first argumant
Code: Select all
$_=$ARGV[0];while($_!=1){for($__=2;$__<$_+2;$__+=2){
if($__==4){$__;}if($_%$__==0){$___=$___.$__." x ";
$_/=$__;last;}if($__>=$_**0.5){$___=$___.$_;$_=1;}}}
$___=~s/x $//;print STDOUT $ARGV[0]," = ",$___,"\n";
the number it factors is the number that's given as the first argumant

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We were reading Heart of Darkness in English class, ...I noticed the page numbers, and remembered the comic, and put two and two together.
My teacher must have been thinking, Wow, he's taking really good notes.
When I picked up my notebook at the end of class, every square inch of the desk had long division on it.
So, being the nerd I am, I soon had a handmade primefactoring program on their TI84.
Oh, and thanks alot muffinking, Im gonna be up til 3:00 am tonight mashing fours together in my brain.
My teacher must have been thinking, Wow, he's taking really good notes.
When I picked up my notebook at the end of class, every square inch of the desk had long division on it.
So, being the nerd I am, I soon had a handmade primefactoring program on their TI84.
Oh, and thanks alot muffinking, Im gonna be up til 3:00 am tonight mashing fours together in my brain.
That, in precise historical terms, sucks.  Bill Sutton
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Apologies for posting to such an old thread, but I felt a dying need to share this (and I registered for the forums just to do it, too!).
Currently, if you type "prime factors" into a google search box that gives suggestions (firefox or google toolbar), the top suggestion will be "prime factors of 1453." I'm not sure if I should be embarrassed for performing the search, or amazed that so many others have done it to get it the top suggestion spot...
Currently, if you type "prime factors" into a google search box that gives suggestions (firefox or google toolbar), the top suggestion will be "prime factors of 1453." I'm not sure if I should be embarrassed for performing the search, or amazed that so many others have done it to get it the top suggestion spot...
hendusoone wrote:Currently, if you type "prime factors" into a google search box that gives suggestions (firefox or google toolbar), the top suggestion will be "prime factors of 1453." I'm not sure if I should be embarrassed for performing the search, or amazed that so many others have done it to get it the top suggestion spot...
Fantastic!
We'll call it the xkcd effect.
err....
0247: "Factoring the Time"
heres the link to the comic http://xkcd.com/c247.html . sorry if its allready been posted I couldnt find it. I've been rereading through the comics and i have to know was 2:53 picked on purpose because its military time 14:53 is prime? when i first read that comic i laughed because of how difficult he had made it for the guy factoring. this time i laughed harder because the first number was prime.

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Re: "Factoring the time" Discussion
Well, I definitely used to do exactly that when looking at the clock, so this comic really hit home for me in a hilarious, dorky way (gotta love being a dork!). I totally understand where you're coming from hendusoone, this is a topic that's definitely worth coming back to (I guess a great deal of the xkcd comics bring up awesome dorky and interesting discussion like this)!
And also, if I may put in a word for primes (as if they need any), they are sooo awesome! One example I use a lot when I get amped up about primes is to think about the ring Z/pZ where p is prime. These are integral domains, as opposed to Z/nZ for all nonprime n, and things that are not integral domains are quite scary. 2*3 should never equal 0 (as in Z/6Z). And of course Z/pZ are also building blocks for finite fields, which are mad cool and trickier to think about than, say, Q or R or C (although C is even cooler  C + the point at infinity is isomorphic to a sphere!)...
OK, one more thing and I'll shut up and actually sleep before morning class, hehe! The algebraic closure of a finite field of characteristic p is the countably infinite field which contains a copy of the field of order p^n for each positive integer n (and is in fact the union of these copies) (according to Wikipedia). I had to show that no finite field is algebraically closed on my algebra exam, and I got curious, and this is a pretty sweet answer (even if only God knows what the above field looks like aside from the given description...) so sue me! Hehe...
And also, if I may put in a word for primes (as if they need any), they are sooo awesome! One example I use a lot when I get amped up about primes is to think about the ring Z/pZ where p is prime. These are integral domains, as opposed to Z/nZ for all nonprime n, and things that are not integral domains are quite scary. 2*3 should never equal 0 (as in Z/6Z). And of course Z/pZ are also building blocks for finite fields, which are mad cool and trickier to think about than, say, Q or R or C (although C is even cooler  C + the point at infinity is isomorphic to a sphere!)...
OK, one more thing and I'll shut up and actually sleep before morning class, hehe! The algebraic closure of a finite field of characteristic p is the countably infinite field which contains a copy of the field of order p^n for each positive integer n (and is in fact the union of these copies) (according to Wikipedia). I had to show that no finite field is algebraically closed on my algebra exam, and I got curious, and this is a pretty sweet answer (even if only God knows what the above field looks like aside from the given description...) so sue me! Hehe...
Re: "Factoring the time" Discussion
What alexk said. I'd already decided that it was going to be prime, so I had a minute to verify that. That's easier than actually factoring the number...
First, you use the usual rules for 2, 3, 5, and 11 (add the digits alternately and see if it's zero).
If 1453 were divisible by 7, so would 1460. Add 140 to get to 1600 which isn't divisible by 7. If 1453 were divisible by 13, so would 1440, which it clearly isn't.
You use similar arguments for each prime, adding multiples till you get to a number that's clearly not divisible. And you're helped once you get near the square root of the number because you know the possible candidate primes that would have to be the other divisor, so you can eliminate them fast (if one's under 40, the other one's over 40...)
Voila, well under a minute. Course, I do this sort of thing a lot.
First, you use the usual rules for 2, 3, 5, and 11 (add the digits alternately and see if it's zero).
If 1453 were divisible by 7, so would 1460. Add 140 to get to 1600 which isn't divisible by 7. If 1453 were divisible by 13, so would 1440, which it clearly isn't.
You use similar arguments for each prime, adding multiples till you get to a number that's clearly not divisible. And you're helped once you get near the square root of the number because you know the possible candidate primes that would have to be the other divisor, so you can eliminate them fast (if one's under 40, the other one's over 40...)
Voila, well under a minute. Course, I do this sort of thing a lot.

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Re: "Factoring the time" Discussion
We should try primefactorizing Graham's number.
...wait, shit.
...wait, shit.
Re: "Factoring the time" Discussion
HOW HAS NOONE BROUGHT UP THAT THE NUMBER GETS BIGGER EVERY MINUTE, NOT EVERY HOUR
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Re: "Factoring the time" Discussion
I don't know if anyone's said this yet or not, but on igoogle there's actually an app you can put on your page that factors the time. It's 100% based on this strip

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Re: "Factoring the time" Discussion
Wow.
You all think the same way *I do*!
You all think the same way *I do*!
Re: 0247: "Factoring the Time"
My and some friends (all physicists) did this a lot on a skiing trip. On the way home at night we tried to do 22:09 as a team effort.
Of course when factorizing numbers of this size you usually get a lot of small factors and maybe one or two in the teens or twenties. Or a prime.
We worked our way up confirming that none of the primes were factors of 2209. After 43 turned out not to divide it and since the next prime would be up at 47, one said: "I think we are past the square root now", so we concluded that 2209 is prime. All agreed.
We were quite embarrassed to learn that 2209 equals 47 squared.
Of course when factorizing numbers of this size you usually get a lot of small factors and maybe one or two in the teens or twenties. Or a prime.
We worked our way up confirming that none of the primes were factors of 2209. After 43 turned out not to divide it and since the next prime would be up at 47, one said: "I think we are past the square root now", so we concluded that 2209 is prime. All agreed.
We were quite embarrassed to learn that 2209 equals 47 squared.

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Re: "Factoring the time" Discussion
tricky77puzzle wrote:We should try primefactorizing Graham's number.
...wait, shit.
Since Graham's number is a power of three, factoring it would be trivially easy:
3 times 3 times 3 times 3 times 3 times 3....
The only tricky part is knowing when to stop. But given that you'll need to repeat the "3 times" waaaaaaay beyond the heatdeath of the universe, I wouldn't worry about that too much.
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