247: Factoring the Time

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Factoring the Time
I occasionally do this with mile markers on the highway.
Title text: I occasionally do this with mile markers on the highway.


Cueball is bored and so he does prime factorize the time shown at the clock. He's been doing this for almost two hours (from 1:00 pm to 2:53 pm). The number 1 is the smallest prime but 253 is in fact not a prime because it can be divided by 11. His co-worker is likely annoyed at this inactivity, and so he switches the clock from 12-hour time (2:53 pm) to 24-hour time (14:53). This makes factorization more difficult, as the time now shown is a four digit number rather than a three digit number. The number 1,453 is a prime number as well, but Cueball has only one minute to solve this.

Finding the prime factors of a number gets exponentially more difficult as the number gets larger.

This comic is also a play on the phrase "factoring the time", which means the time required to do something or the current time into account when making a decision.

The title text refers to doing something similar with mile marker signs, hopefully not while driving as this could be considered distracted driving.


[One man is sitting at a computer. Cueball sits at a separate desk. There is a clock which reads 2:53.]
Cueball: 253 is 11x23
Man at computer: What?
Cueball: I'm factoring the time.
Cueball: I have nothing to do, so I'm trying to calculate the prime factors of the time each minute before it changes.
Cueball: It was easy when I started at 1:00, but with each hour the number gets bigger
Cueball: I wonder how long I can keep up.
[Man at desk reaches back and touches the clock.]
[Clock now reads 14:53.]
Cueball: Hey!
Man at computer: Think fast.


  • There is a widget for OS X to display the current time and its prime factors.

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I used to find the prime factors of the remaining distance until the next turn. It starts off difficult (for me) at 99 miles, etc. When it gets down to 30 miles, it gets easier. Then, at 9.9 miles, I have a tenth the time to factor 99 again, and it gets easier as the numbers get smaller. This is actually a pretty good way to pass the time while driving. (talk) (please sign your comments with ~~~~)

Paying attention to your driving might be a benefit. To yourself and others. Just sayin'.Jakee308 (talk) 20:00, 24 April 2015 (UTC)

I wonder how much time Randall spent trying to find a time that is not prime but the time + 1200 would be. -- Flewk (talk) (please sign your comments with ~~~~)

Took me about 5 minutes with a script after getting a list of primes from the internet: 1:19; 1:21; 2:09; 2:47; 2:53; 2:59; 3:23; 3:43; 4:07; 4:13; 4:27; 4:37; 5:33; 5:53; 5:59; 6:11; 6:23; 7:07; 7:13; 7:31; 7:49; 8:03; 8:17; 9:13; 9:31; 9:43; 10:03; 10:07; 10:37; 10:43; 11:11; 11:33; 11:39; 11:41; 11:47; 11:57 (also the technical cases of: 12:03; 12:05; 12:07; 12:11; 12:19; 12:41; 12:43; 12:47; 12:53) . -- 06:18, 20 January 2016 (UTC)

You know, in the state of Massachusetts, which is where Randall said he lives in the book What If?, mile markers on the highway are placed every 0.2 miles, so he would get only twelve seconds per marker if he's trying to do each and every one (less if he's slightly speeding like everyone else does when there's no traffic). 02:09, 22 February 2016 (UTC)

I added another explanation for the title text. It seems to me that factoring the (often same) mile marker numbers is a bit boring. Lanmi (talk) 11:55, 23 April 2016 (UTC) Lanmi

Why would factoring become secondary problem after switching to km?