0247: "Factoring the Time"

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warriorness
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0247: "Factoring the Time"

Postby warriorness » Wed Apr 11, 2007 4:05 am UTC

Image
Alt text: I occasionally do this with mile markers on the highway.

When I was in seventh grade, my math teacher had our class "warm-up" by making equations out of the date. For example, if the date were 3/14/02, a solution could be "3+1-4 = 0*2".

It was 2001 in the fall semester, and eventually somebody realized that since all the dates ended in "01" they could just take the first couple of numbers, do whatever they wanted with them, raise it to the 0 power and set it equal to 1. A rule against doing that was made very quickly, and alternative solutions had to be found.

I still do this very frequently. For example, just today (!) I figured that for all the days this month in the interval [10, 19], you could just take log-base-4 of 1 (which is zero btw), and use the zero from the year in multiplication so you'd have 0=0.

(1453, by the way, is prime.)
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Postby SNAFU » Wed Apr 11, 2007 4:10 am UTC

God, I do this all the time with random numbers. Also, when I'm bored and have nothing to read, I try to count prime numbers as high as possible.
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Postby Locus Cosecant » Wed Apr 11, 2007 4:11 am UTC

Oh geez, I do this all the time. Show me a number between 30 and 3000 and my first instinct is to factor it into a product of primes.


Well, I guess that's not really the same thing as is happening in the comic, but still.

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Postby Oort » Wed Apr 11, 2007 4:23 am UTC

Locus Cosecant wrote:Oh geez, I do this all the time. Show me a number between 30 and 3000 and my first instinct is to factor it into a product of primes.


Well, I guess that's not really the same thing as is happening in the comic, but still.


1372.

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Postby TonyD » Wed Apr 11, 2007 4:28 am UTC

Oort wrote:1372.


2 * 2 * 7 * 7 * 7

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Postby Keenan Pepper » Wed Apr 11, 2007 4:28 am UTC

Aaargh! Clock times are base sixty, not base ten. 2:53 is prime (173), and 14:53 (893) is 19 times 47.

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Postby EvanED » Wed Apr 11, 2007 4:32 am UTC

Given that the clock displays hours in 24 hour time (as evidenced by the 14:53), I'm going to assume that it is 2:53 am in the comic. I thus have a suggestion for Mr. "I have nothing to do" Stick Figure: sleep!

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Postby TonyD » Wed Apr 11, 2007 4:33 am UTC

EvanED wrote:Given that the clock displays hours in 24 hour time (as evidenced by the 14:53), I'm going to assume that it is 2:53 am in the comic. I thus have a suggestion for Mr. "I have nothing to do" Stick Figure: sleep!

I'm pretty sure he *switched* it to 24-hour time.

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Postby d3adf001 » Wed Apr 11, 2007 4:35 am UTC

so why are they at work at 2:53 in the morning? also shouldnt that be the guy in the hat?

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Postby thefiddler » Wed Apr 11, 2007 4:38 am UTC

Yes, he switched the clock from 12 hour AM / PM to 24 hour time. (As indicated by the *beep*.)

I've never done this before and don't plan on starting. I am not that mathematically inclined. :oops:

*self-imposed ban of shame*

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Postby hermaj » Wed Apr 11, 2007 4:42 am UTC

EvanED wrote:Given that the clock displays hours in 24 hour time (as evidenced by the 14:53), I'm going to assume that it is 2:53 am in the comic. I thus have a suggestion for Mr. "I have nothing to do" Stick Figure: sleep!


2:53am = 02:53
2:53pm = 14:53.

I do not do this ever. I would get lost halfway and end up curled up in the foetal position, rocking back and forth, yelling "Make the numbers stop!" It is for the best.


EDIT: I should probably take less time writing my posts :P That whole thing was explained while I was still pondering (read: playing KOL).

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Postby EvanED » Wed Apr 11, 2007 4:47 am UTC

Ahhhh, that makes more sense.

I figured the other stick figure guy was changing the time so it was wrong... I tend to read things quickly (it's one of my bad qualities) and didn't notice the correspondence. Oopsie.

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Postby d3adf001 » Wed Apr 11, 2007 4:50 am UTC

oh i thought he just added 12 hours as in pushed the button 12 times and thats why it beeped

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thanks for ten seconds of distraction...

Postby gnarayan » Wed Apr 11, 2007 4:54 am UTC

#!/bin/csh
#
set i=0
set limit=2400
while ( $i < $limit )
factor $i
@ i = $i + 1
end

ok back to lab work...

You could write an awk script if you want to use sexagesimal...

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Postby JuliaGlass » Wed Apr 11, 2007 4:54 am UTC

I can safely say I've never had any sort of fascination with prime numbers. I play number and word games, but they have little mathematical merit.

Sometimes it feels like I don't really have a language and everything is just a frantic translation. I'm always translating words into numbers and numbers into music and music into pictures and pictures into words and so on without actually latching on to one method of expression.

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Postby MrBawn » Wed Apr 11, 2007 5:01 am UTC

Wow, I thought I was being kinda geeky today when I pointed out that it was "airplane time."

Incidentally, my other favorite time of day is "pi time."

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Re: "Factoring the time" Discussion

Postby Twasbrillig » Wed Apr 11, 2007 5:02 am UTC

warriorness wrote:(1453, by the way, is prime.)


GKJEASFJASFJET!!!

Thanks for ruining what I was totally going to be all smug about.

I cannot believe... just, gah!

I wanted to claim that! :(
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Postby RandomPrecision » Wed Apr 11, 2007 5:29 am UTC

Not that it's relevant to clocks, but 8675309 is prime.

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Postby asliceofpi » Wed Apr 11, 2007 5:29 am UTC

I used to play 24 with the time when I couldn't sleep. It was very frustrating to lie there at 11:17 just to wait for 11:18 so it would work. :P

I don't think I've ever been good enough at factorization to be able to do that in time, though.

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Postby EvanED » Wed Apr 11, 2007 5:36 am UTC

d3adf001 wrote:oh i thought he just added 12 hours as in pushed the button 12 times and thats why it beeped


Good, I'm glad I'm not the only one. ;-)

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Postby Joshua » Wed Apr 11, 2007 5:44 am UTC

RandomPrecision wrote:Not that it's relevant to clocks, but 8675309 is prime.


That's cool.
Here's another interesting prime number fact.

The following numbers are prime:
3331333
3333133
3333313
3333331

Who knows why?! (ermm... besides that it doesnt, y'know, factor otherwise)

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prime numbers game

Postby kneser » Wed Apr 11, 2007 5:45 am UTC

When I was little, we played a game with prime numbers. We called it ping pong. First, you would assign ping and pong a prime number. We used ping=2, pong=3. Then you would start counting starting with one. But instead of saying 2 or any factor of 2, you would say ping.

For instance:
1, ping (2), pong (3), ping (4), 5, ping pong (6), 7 and so on so only the prime numbers would be said as numbers.

Anyways, this is what I do when I'm bored.

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Postby Ash » Wed Apr 11, 2007 5:46 am UTC

I do this a lot. Especially when I'm drunk. Also when I was in hospital once, I couldn't sleep so I tried factorising my 11 digit patient number in my head. I accidentally changed a number after about 3 hours, and never got any sleep.

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Postby Daem0hn » Wed Apr 11, 2007 5:53 am UTC

reminds me of Kira's number/time game :P i wonder if it is based on her much like one of the previous comics was.....
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Postby engine » Wed Apr 11, 2007 5:57 am UTC

The guy working at the computer should definitely be wearing the hat.

"The" hat.

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Postby Patashu » Wed Apr 11, 2007 6:06 am UTC

I can safely say that I've -never- factorized numbers for fun.

I like the comic anyway. Poor 24 hour time.

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Re: "Factoring the time" Discussion

Postby OneLess » Wed Apr 11, 2007 6:59 am UTC

xkcd wrote:[
Alt text: I occasionally do this with mile markers on the highway.

I use the mile markers to either a) try to see how accurately I can count off seconds by matching my counting with the vehicle's speed or b) see how close of an approximation I can make to the vehicle's actual speed by judging the mile markers. Or I just listen to the radio like a normal human being, but there's no pizazz in that.

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Postby Rocco » Wed Apr 11, 2007 7:14 am UTC

I think the alt text should warn the reader not to attempt to factor 1453, as it is prime. Wasted effort, but good for a chuckle. That's what I get for not reading the forum first.

(Come to think of it, it still would have been a wasted effort even if I had been able to factor it. Such is the pointlessness of recreational math.)

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Postby Xayma » Wed Apr 11, 2007 7:20 am UTC

I had it easy when I read this comic:

5:14 = 2 * 257
5:15 = 5 * 3 * 37
5:16 = 2 * 2 * 3 * 43

I would die if it was in 24 hour time, because 1714 isn't as easy (well its 2 * 857 which is also prime) but the others aren't as easy.

Ahh 5:14 how you are easy.

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Postby skeptical scientist » Wed Apr 11, 2007 8:23 am UTC

Is there any way to figure out 1453 is prime in less than a minute without resorting to a calculator? I figured it wasn't divisible by any prime less than 13, and then decided it was probably prime, but it seems pretty much impossible to see it's prime in your head.
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Postby killerstar » Wed Apr 11, 2007 9:04 am UTC

You could make a small program wich tells you if a number you enter is prime or not . I've done it a day I had nothing to do. (in VB6, pleace don't hate me)

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Postby skeptical scientist » Wed Apr 11, 2007 9:23 am UTC

Yeah, that's what I did. I meant a way of doing it in your head.
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Postby iw » Wed Apr 11, 2007 10:13 am UTC

skeptical scientist wrote:Yeah, that's what I did. I meant a way of doing it in your head.
Become autistic?

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Postby LLCoolDave » Wed Apr 11, 2007 10:34 am UTC

Well, it's something that can be done with a bit of exercise.

First of all, it is obvious that 1453 is a prime number for humoristic purpose. However, to factor a number in my head, I usually use the following strategy:

1) Get an approximation of the square root of the number. In this case, it is a bit under 40, so 37 is the highest potential factor of the number.
2) There are rules to figure out if a number is divisible by certain factors for numbers up to at least 100, but I doubt you know many. If you do, feel free to use them, but they are no necessity.
3) Don't try to divide the number by each possible factor. Instead, first try to figure out if it is divisible before calculating the exact outcome of the division. This means that if you are trying to figure out if m is divisible by n, you can add or substract multiples of n to m as you please, and divide m by any factor that might come in handy. If you end up with a multiple of n at the end, the original number is divisible by n, so you can now do an exact calculation.

Example: To figure out if 1453 is divisible by 17, first add 17 so you have 1470. Divide by 10 => 147. Substract 17 => 130. Divide by 10 => 13, which is obviously not a multiple of 17.

I'm aware this is likely not the fastest or most efficient way to do it, but it's something most people should be able to do in their head without special training, as long as you can remember one or two numbers while doing mental calculations. With a bit of training, it should be possible to factor most times within a minute.

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Postby evilbeanfiend » Wed Apr 11, 2007 10:42 am UTC

engine wrote:The guy working at the computer should definitely be wearing the hat.

"The" hat.


i think you have invented a new phrase - i'm certainly the one who wears the hat around here.
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Postby macronencer » Wed Apr 11, 2007 10:48 am UTC

I really enjoyed this one! Thanks.

Way back in my teen years (that's around the early 1980s) I had a ZX Spectrum computer. I wrote a prime factorizer for it, and the first number I entered was my phone number (in those days, in that location, it was six digits: 678479).

Turns out 678479 is prime. That spooked me a little, at the time. The first number I tried :\
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Postby tloicto » Wed Apr 11, 2007 10:52 am UTC

Way back when at swim practice (before we had to memorize the squares of numbers through 30 for one of my math classes, so computing the square actually took a non-trivial amount of time), rather than just keeping track of what number length/thing of the set we were on I'd square the number. So when one of the people in my lane would ask what number we were on I'd say the square. No one really got it.

Factoring for the hell of it, though...never really been something I've done.
Last edited by tloicto on Wed Apr 11, 2007 10:53 am UTC, edited 1 time in total.

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Postby apricity » Wed Apr 11, 2007 10:52 am UTC

engine wrote:The guy working at the computer should definitely be wearing the hat.

"The" hat.


It's out of dress code at work.

I would *totally* be that guy at the computer though. Factor-guy is smart and all, but computer-guy is cunning. Much cooler.
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Postby cmacis » Wed Apr 11, 2007 11:26 am UTC

When I wrote a program to find primes (sieve of Erastrones, up to square root), and then wrote a program to read the output files line by line since they got too large for notepad, I was gutted to see that I was so close to being born on a prime year. I was so close to pi day that my birthday counts as a pi approximation (using american date format mm/dd)
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Postby Yakk » Wed Apr 11, 2007 1:22 pm UTC

There are only 7 primes over 11 up to 40.

13 17 19 23 29 31 37

So long as you know the quick tricks for determining "divisible by X", you can detect primality on every number up to 1600. :)


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