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I think it helps to remember that 3 times 7 is 21. When I think about that it looks less wrong.
It's the stupid seven multiplication table. Whatever glitch in human software makes it look so much less intuitive than all the others messes with so many other things that should be easy. I swear I struggle every time I have to look at it. I had to double check seven times three multiple times right now.
I don't think that actually helps, because it's all vibes. 51 looks prime, because of no reason at all, and absolutely nothing looks like it should be divisible by 17, again, because raisins.
Knowing why it's true doesn't make it look right.
The digit sum of 51 is 6, which is divisible by three. So 51 is also divisible by three. It’s not even hard to see that it’s not prime.
Yup, my personal prime check is:
- Even?
- Ends in 5?
- Digits sum to 3?
If it fails all three and it's not an "obvious" prime (<20), then it's prime enough for me.
Also
Ends in 0,
but that's covered by 5 really.
It's also covered by being even.
But I can wrap my head around that 51 is divisible by seventeen because of 21 and seven plus something that deals with the remaining 30 somewhere.
I know that's not how it works, but as you say it fixes my vibes when I see the 21 hiding inside the 51.
I'll say this: the other thing that makes this one a hard pill to swallow is that 17 looks way too big, and my vibes fix doesn't address that, but hey.
Why not add the digits? If the sum of digits is divisible by 3, the number is divisible by 3. 5 + 1 is divisible by 3, so it's not prime.
49 "looks" more prime to me because it fails that test, and if I didn't know it's 72, I'd say it's probably prime.
I think the posts along these lines are already two steps too far away from the vibes.
Nobody is even considering the number being prime, it just looks like there can't be a round number of one against the other because one is big and ends in seven and the other is relatively small and ends in 1.
If you're even thinking about divisibility rules you're doing it wrong. As in, your brain is too impacted by maths to see what the numbers look like from instinct alone. There's no thinking in this, they just look weird together.
I've always loved math, so seeing patterns is intuitive. 3 also happens to be my favorite number, so I like looking for it in the wild.
If someone says "51 is divisible by 17," my instinct is that it tracks because it's obviously divisible by 3, so the other factor would be a little less than 20. That's literally my first instinct.
7 is a weird multiple, but 3 is really easy. I guess I'm weird...
If there’s a number that’s the most oddball in the multiplication table, it’s 7.
It’s a prime number that doesn’t share any common divisors with 10, and isn’t adjacent to a divisor of 10 either.
2 and 5 are common divisors of 10, so they’re piece of cake.
3 is so small and close to 2, so it’s not too difficult to get.
9 is one off from 10, so it has a very predictable pattern.
4, 6 and 8 are even numbers, so they share common divisors with 10.
3 is easy because of the "digits sum to 3" trick, if you get stuck counting by 3s, it's easy to reset. Oh, and the proof for this is based on our 10-based number system, so your point absolutely stands.
I have to remember it in patterns.
Digits go:
7, 4, 1
8, 5, 2
9, 6, 3
0
Tens go:
0, 1, 2
2, 3, 4
4, 5, 6,
7
Then my brain recognises everything else and I can't explain it properly 😂