Showerthoughts

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A "Showerthought" is a simple term used to describe the thoughts that pop into your head while you're doing everyday things like taking a shower, driving, or just daydreaming. The best ones are thoughts that many people can relate to and they find something funny or interesting in regular stuff.

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Amazon should've made Prime Day fall on a date corresponding to an actual three-digit prime number. (sh.itjust.works)

submitted 4 months ago* (last edited 4 months ago) by [email protected] to c/[email protected]

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Amazon is running a Prime Day sale on July 16 and 17. Setting aside the fact that this is two separate days, neither 716 nor 717 are prime numbers. They should've done 7/19 instead.

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[–] [email protected] 2 points 4 months ago (1 children)

It works for 9, too.

[–] [email protected] 2 points 4 months ago

If you're looking for a proof:

Our base 10 system represents numbers by having little multipliers in front of each power of 10. So a number like 1234 is 1 x 10^3 + 2 x 10^2 + 3 x 10^1 + 4 x 10^0 .

Note that 10 is just (3 x 3) + 1. So for any 2 digit number, you're looking at the first digit times (9 + 1), plus the second digit. Or:

(9 times the first digit) + (the first digit) + (the second digit).

Well we know that 9 times the first digit is definitely divisible by both 3 and 9. And we know that adding two divisible-by-n numbers is also divisible by n.

So we can ignore that first term (9 x first digit), and just look to whether first digit plus second digit is divisible. If it is, then you know that the original big number is divisible.

And when you extend this concept out to 3, 4, or more digit numbers, you see that it holds for every power of 10, and thus, every possible length of number. For both 9 and 3.