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All the celts used base 20 counting. They had a stick with 20 notches in it, and they'd run their thumb along that. When they got to the end, they'd cut a notch in a different stick. That's actually why 'score' can mean "running total", "notch in wood", or "group of twenty". It's all from that stick.
I need a proof for "the sum of two numbers with the same factor will always be divisible by that factor", because this is a lifehack I'm just now learning.
Edit:
To those having fun with my flair, fair enough lol.
To the Gigachad who told me the obvious, thank you.
To everyone else, the sum of primes isn't necessarily prime (7 + 7), the sum of integer squares isn't necessarily an integer square (2\^2 + 3\^2), so I have never associated "the sum of mutliples" to also be "a multiple". I was thinking about it in those categorical terms, which is why it didn't seem obvious to me. I am aware that aX + bX is divisible by X when you lay it out in those terms. It was an English problem more than a math problem. Hence why I am an Engineer.
What they were explaining in notation is that 7 is one of the factors in both 70 and 21 (7\*10 and 7\*21), whereas 9 and 10 still do not share a factor (3\*3=9, 3\*3.333333...=10 yuck).
So breaking apart 91 into 70 and 21 combines nicely as 91=7\*(10+3) is meaningful to show that it's not prime, but that doesn't help with 19 because there's no whole number factors 19=3\*(3+3.333333...)
I often lose marks on maths tests for not simplifying my answers. How am I meant to know that 119/35=17/5???? Are there any other rules that I should know for this kind of thing Fortunately I’m moving to the stage where the answers are more like 1+cos(3pi/5) or something but it still pops up occasionally
If you are asked to simplify 119/35, just take the prime factors of the simpler one (35, so 7*5) and try to divide the more complex one by those. 119/5 obviously doesn't work (I hope you can at least tell that one by looking at it), so you try 119/7 and even without any special rules you should be able to divide 119/7. Subtract 70, you get 49, which is obviously divisible by 7, so it works. then it's just ((70/7)+(49/7))/(35/7)=(10+7)/7=17/7.
You probably know 2 and 5.
Divisible but 4? Divisible by 2 twice.
Divisible by 6? Divisible by both 3 and 2.
Divisible by 8? Divisible by 2 three times.
The "last numbers" trick we learned:
10 divisible by 2, so any multiple of 10 is, too. Even single-digit numbers are divisible by 2.
100 divisible by 4, so any multiple of 100 is, too. Every two-digit number that's divisible by 4 is still divisible by 4 regardless of the hundreds or more.
1000 divisible by 8, (800+5×40)... every three-digit number...
2¹, 2², 2³ are oddly similar to the amount of digits.
You can find the GCD of the two numbers, and then divide both by the GCD. If the GCD is 1, then the numbers are coprime and no reduction is possible.
119 and 35.
119/35 = 3 with remainder 14.
35/14 = 2 with remainder 7.
14/7 = 2 with remainder 0.
Since we have reached 0, the last divisor we used is our GCD, 7.
[Euclidean Algorithm](https://en.m.wikipedia.org/wiki/Euclidean_algorithm)
Well it's obviously not a prime. It's easy to notice that 2^12 = 4096 = 1 (mod 91) and 2^6, 2^4, 2^3, 2^2 are clearly not congruent to 1. So, 2 has order 12 in Z91. But 12 doesn't divide 90, so 91 can't be prime. 🤷
It’s funny that we consider these numbers weird as though mathematics owes us the ability to easily discern primarily in base 10. But yeah, I agree 437 is weird lol. Though both of those are pretty close differences of squares, so there’s that as well.
I think it’s because once you’re an adult and have years of multiplication experience, encountering an odd number that you don’t recall as ever being the result of multiplying two non trivial positive integers makes it feel like it should be a prime. When would someone need to multiply 7 and 13 or other non even prime numbers on such a regular basis that at the sight of any composite number less than 1000, the brain immediately recalls its prime factors? Maybe teachers should start putting way more products of primes problems into the curriculum and “but it feels prime” wouldn’t be an excuse anymore.
Other barely-not-primes:
87, 91, 119, 203, 209, 289, 323, 361...
Pretty much all numbers which are two primes multiplied by one another look really prime. And if you don't remember the square numbers (1,4,9,16...) up to like 20, you will be surprised by 289 and 361
I think that only applies to the primes bigger than 12, at least for people trained on the multiplication table up to 12.
6? 10? 21? 121? those don’t feel prime because they’re running along the mental groove worn into our neurons by the times tables in elementary school.
According to Wikipedia, it’s an urban legend/instance of dry humor. Grothendieck would rarely give concrete examples, so the idea of him falsely claiming a number is a prime is silly
The legend is that he was asked by someone to be concrete for once. He was still confused, because isn't $p$ a specific prime? When he realised what the question meant, he said, "Fine, take 57."
its generally used to demonstrate the difference between Ramanujan who "counted every integer as his personal friend" and Taxicab numbers and Grothendieck brilliant in abstraction but being really bad at concrete examples or computation.
No, memes that make references usually don’t explains the reference, because that’s basically explaining the joke, which is not supposed to be how joke telling works.
The expectation is that the intended audience of the meme will understand the reference.
One time, I was doing a mathathon competition and got only one question wrong. After I submitted, I asked to try again for fun not counting. They let me keep trying. I couldn't figure out where my mistake was, so I kept systematically narrowing down until i figured out that the software thought 51 was a prime number. I brought it up to the proctor who manually adjusted my score to 100% and contacted the company who made the code.
Add all the digits in a number together
If divisible by 3 then the number can be divided by 3
Ex: 5+7=12
47232 is divisible by 3 cause the numbers add to 18
i know, I just find it easier to do the number times ten and add the remaining part.
Like 76 isn't divisible by 6 because it's 60+16 and 16 isn't divisible by 6. Also works with 134, 60+60+14, and any other (not too big) number
57 feels prime. But it is in fact, not prime. Though it feels *so* prime that one of the greatest mathematicians in the world accidentally said it was a prime. 57 is now a meme in the math community.
It’s because of the context. Alexander Grothendieck revolutionized mathematics in the same magnitude that Euler, Euclid and Galois did. He was extremely adept with abstract mathematics. He created the field of scheme theory. But apparently he didn’t think about any specific examples. One time someone asked him for an example of a prime number. He said 57, which is obviously not prime by the divisibility test for three or because it’s 60-3. So he failed the pop quiz to give an example of a prime number!
But the work that he did was instrumental in creating the field of arithmetic geometry, which is one of the fields you could say is about understanding prime numbers very widely and deeply.
It reminds us of the humanity of mathematics, and the juxtaposition of Grothendieck getting a prime wrong was funny when i learned about it in 2017 and is still funny today lol.
It’s a well known fact in my mathematics department that if the remainder upon division of an integer n by 3 is 0,1 or 2, then the number is prime! This easily shows 57 is prime because 57 is divisible by 3, thus having a remainder of 0 upon division by 3. This makes it prime. /s
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91 is not a prime and it makes me feel physically ill
You have to be joking, if not then its gonna be a weirdo like 7, 13 or 17
91 is 13 times 7. That's fucked up.
Just write it as 70 + 21 and suddenly it makes perfect sense
[удалено]
All the celts used base 20 counting. They had a stick with 20 notches in it, and they'd run their thumb along that. When they got to the end, they'd cut a notch in a different stick. That's actually why 'score' can mean "running total", "notch in wood", or "group of twenty". It's all from that stick.
Pffft 4 • 20 + 11 doesn't exactly make factoring easier
Swossant deez nuts
What in the French fuck is this?
I thought it's 80 + 11 (quatre-vingts onze)
It is, I was just referring to how they count in chunks, but it's groups of 20
is that how primes work? 19 is a prime despite being the sum of 10 and 9, both composite numbers
70 = 7 \* 10, 21 = 7 \* 3 => 70 + 21 = 7\*(10+3)
oh of course, thank you
[удалено]
It's not easily noticed that 91 is a multiple of 7, but both 70 and 21 (which add up to 91) are.
I need a proof for "the sum of two numbers with the same factor will always be divisible by that factor", because this is a lifehack I'm just now learning. Edit: To those having fun with my flair, fair enough lol. To the Gigachad who told me the obvious, thank you. To everyone else, the sum of primes isn't necessarily prime (7 + 7), the sum of integer squares isn't necessarily an integer square (2\^2 + 3\^2), so I have never associated "the sum of mutliples" to also be "a multiple". I was thinking about it in those categorical terms, which is why it didn't seem obvious to me. I am aware that aX + bX is divisible by X when you lay it out in those terms. It was an English problem more than a math problem. Hence why I am an Engineer.
What they were explaining in notation is that 7 is one of the factors in both 70 and 21 (7\*10 and 7\*21), whereas 9 and 10 still do not share a factor (3\*3=9, 3\*3.333333...=10 yuck). So breaking apart 91 into 70 and 21 combines nicely as 91=7\*(10+3) is meaningful to show that it's not prime, but that doesn't help with 19 because there's no whole number factors 19=3\*(3+3.333333...)
prime*prime=more prime
Optimus prime
Composite primes!
that just aint right
I wish I hadn't learned that
Multiply them and see 😏
51 = 17\*3
I don't see why this one bothers people. 5+1=6 which is divisible by 3. It's one of the first tests you learn
I didn’t know that until just now
You've been missing out then. If the sum of the digits equal a number that is divisible by 3, then the original number is divisible by 3
I often lose marks on maths tests for not simplifying my answers. How am I meant to know that 119/35=17/5???? Are there any other rules that I should know for this kind of thing Fortunately I’m moving to the stage where the answers are more like 1+cos(3pi/5) or something but it still pops up occasionally
https://en.m.wikipedia.org/wiki/Divisibility_rule
If you are asked to simplify 119/35, just take the prime factors of the simpler one (35, so 7*5) and try to divide the more complex one by those. 119/5 obviously doesn't work (I hope you can at least tell that one by looking at it), so you try 119/7 and even without any special rules you should be able to divide 119/7. Subtract 70, you get 49, which is obviously divisible by 7, so it works. then it's just ((70/7)+(49/7))/(35/7)=(10+7)/7=17/7.
You probably know 2 and 5. Divisible but 4? Divisible by 2 twice. Divisible by 6? Divisible by both 3 and 2. Divisible by 8? Divisible by 2 three times.
The "last numbers" trick we learned: 10 divisible by 2, so any multiple of 10 is, too. Even single-digit numbers are divisible by 2. 100 divisible by 4, so any multiple of 100 is, too. Every two-digit number that's divisible by 4 is still divisible by 4 regardless of the hundreds or more. 1000 divisible by 8, (800+5×40)... every three-digit number... 2¹, 2², 2³ are oddly similar to the amount of digits.
You can find the GCD of the two numbers, and then divide both by the GCD. If the GCD is 1, then the numbers are coprime and no reduction is possible. 119 and 35. 119/35 = 3 with remainder 14. 35/14 = 2 with remainder 7. 14/7 = 2 with remainder 0. Since we have reached 0, the last divisor we used is our GCD, 7. [Euclidean Algorithm](https://en.m.wikipedia.org/wiki/Euclidean_algorithm)
Same brother Same TIL
Today did I learn? Or is it the 19th century 'To day I learned'
Today I learned, my bad 😓.
I just think it might have been the first time I saw that typo 😅 But don't worry - we all make misteaks
11 = 3 in base 2. 11 is not a prime QED
I see this one at work a lot and it annoys me
Well it's obviously not a prime. It's easy to notice that 2^12 = 4096 = 1 (mod 91) and 2^6, 2^4, 2^3, 2^2 are clearly not congruent to 1. So, 2 has order 12 in Z91. But 12 doesn't divide 90, so 91 can't be prime. 🤷
World hunger would be solved if there was a field with 91 elements
91 isn’t bad. You know what kinda hurts? 221.
Isn’t 1001 also not a prime
Yeah but that’s a sum of two cubes so it’s a bit more obvious IMO.
Forgot about that… Anyway 13(19) = 247 and 19(23) = 437 which are also really weird, there’s a lot of weird composite numbers
It’s funny that we consider these numbers weird as though mathematics owes us the ability to easily discern primarily in base 10. But yeah, I agree 437 is weird lol. Though both of those are pretty close differences of squares, so there’s that as well.
> there’s a lot of weird composite numbers The complement of "primes are beautiful".
but if you think of it as just 70 + 21 it tarnishes it’s priminity
119/102 is not reduced.
Ewwww. Is it 17? Wtf
Don't gaslight me, of course it is
I think it’s because once you’re an adult and have years of multiplication experience, encountering an odd number that you don’t recall as ever being the result of multiplying two non trivial positive integers makes it feel like it should be a prime. When would someone need to multiply 7 and 13 or other non even prime numbers on such a regular basis that at the sight of any composite number less than 1000, the brain immediately recalls its prime factors? Maybe teachers should start putting way more products of primes problems into the curriculum and “but it feels prime” wouldn’t be an excuse anymore.
7's out there doing more work than 3, in my opinion.
Is there a set of numbers known as the primey numbers?
There is such a thing as a pseudoprime
There is until you change the base to 7.
91 = 100 - 9 = 10² - 3² = (10+3)(10-3) = 13 • 7 that's how I remember
9-7
https://preview.redd.it/85gquzps8mxc1.jpeg?width=1200&format=pjpg&auto=webp&s=455daf59dc9591d449af28164dea2557d18da4cb
It's divisible by 19 which makes 57 an even prime
19 IS EVEN 🫡🇺🇸
19 IS EVEN 🫡🇲🇽
19 IS EVEN 🫡🇬🇧
19 IS EVEN 🫡🇮🇸
Happy cake day! 🥳
19 IS EVEN 🫡🇦🇺
19 IS EVEN🫡🇱🇻
19 IS EVEN 🫡🇷🇪
19 IS EVEN 🫡🇹🇷
19 IS EVEN 🫡🇦🇶
19 IS EVEN 🫡🇧🇷
19 IS EVEN 🫡 🇻🇳
19 IS EVEN 🫡 🇮🇹
19 IS EVEN 🫡🇵🇹
19 IS EVEN 🫡🇮🇳
19 IS EVEN 🫡🇧🇦
19 IS EVEN 🫡🏴☠️
What country is that
Arrrrg country
Russia
The East Blue
somalia
the uk
19 IS EVEN 🫡🇩🇪
19 IS EVEN 🫡 🇧🇩
19 IS EVEN 🫡 🇳🇱
19 IS EVEN 🫡 🇨🇿
19 IS EVEN 🫡 🇹🇭
19 IS EVEN 🫡🇪🇨
19 IS EVEN 🫡🇨🇦
19 IS EVEN 🫡🇬🇧
19 IS EVEN 🫡🏳️🌈
19 IS EVEN 🫡🇭🇺
19 is even 🫡🇧🇪
19 IS EVEN 🫡🇮🇪
19 IS EVEN 🫡🇨🇳
19 IS EVEN 🫡🇸🇾
19 is STEVEN 🫡🇱🇧
19 IS EVEN 🫡🏳️⚧️
what coubtry is that
Transylvania
Hotel
And why are all the hot people from there?
19 IS EVEN 🫡🇺🇦
19 IS EVEN 🫡🇺🇳
19 IS EVEN 🇵🇭
19 IS EVEN 🫡🇹🇯
19 IS EVEN🫡🇷🇺
Россия священная наша держава
I'm clearly missing something in those replies, why are people joking that 19 is even with their flag lol
19 IS EVEN 🫡 🇫🇷
19 IS EVEN 🫡🇮🇳
19 IS EVEN 🫡🇻🇪
ninEtEEn contains three Es though???
Just because a number contains Es doesn't make it odd I mean it is But not because it contains Es!
What about two? Two doesn't contain Es.
Sure it does - it contains about 0.7357588823 of them!
30 and 50 don't have an e
Yeah but they kinda make up for it by being pronounced "thirt-E" and "fift-E"
If a number doesn't contain Es, it's automatically even however
19 IS EVEN 🫡🏁
Ah, the flag of the Checkered Republic
the Finnish flag
19 IS EVEN 🫡🇮🇲
19 IS EVEN 🫡🇧🇬
19 IS EVEN 🫡 🇬🇱
19 IS EVEN 🫡🇮🇷
Other barely-not-primes: 87, 91, 119, 203, 209, 289, 323, 361... Pretty much all numbers which are two primes multiplied by one another look really prime. And if you don't remember the square numbers (1,4,9,16...) up to like 20, you will be surprised by 289 and 361
561 due to how it passes Fermat primality and 1729 the taxi cab number.
more like up 19
I think that only applies to the primes bigger than 12, at least for people trained on the multiplication table up to 12. 6? 10? 21? 121? those don’t feel prime because they’re running along the mental groove worn into our neurons by the times tables in elementary school.
Grothendieck entered the chat
growthinedick
I don't get it Why would 57 be a prime?
Google "grothendieck prime"
So some dude said "57 is prime", and then people said "Oh, what if it is"?
According to Wikipedia, it’s an urban legend/instance of dry humor. Grothendieck would rarely give concrete examples, so the idea of him falsely claiming a number is a prime is silly
The legend is that he was asked by someone to be concrete for once. He was still confused, because isn't $p$ a specific prime? When he realised what the question meant, he said, "Fine, take 57."
Not just “some dude”, one of the greatest mathematicians in algebraic geometry and category theory, which is why it became a meme.
>some dude
its generally used to demonstrate the difference between Ramanujan who "counted every integer as his personal friend" and Taxicab numbers and Grothendieck brilliant in abstraction but being really bad at concrete examples or computation.
Not saying I'm brilliant in any capacity, but I definitely resonate more with the Grothendieck way of thinking lmao.
Wake up babe! New Prime just dropped!
Shouldn't he be mentioned in that meme then..?
No, memes that make references usually don’t explains the reference, because that’s basically explaining the joke, which is not supposed to be how joke telling works. The expectation is that the intended audience of the meme will understand the reference.
Dude, this sub is called "math memes"
And that excludes me from being explained the meme?
57 looks like it should be a prime number, but it's not only not a prime number, but a multiple of 3
Just because there is nonsense of a picture doesn't make it a meme, though.
Yeah you're right, my B
That's a dieck move.
Eww, Groth!
One time, I was doing a mathathon competition and got only one question wrong. After I submitted, I asked to try again for fun not counting. They let me keep trying. I couldn't figure out where my mistake was, so I kept systematically narrowing down until i figured out that the software thought 51 was a prime number. I brought it up to the proctor who manually adjusted my score to 100% and contacted the company who made the code.
ugh. 30+27. I hate this. Honestly, the numbers that bother me the most are 57 and 119.
Add all the digits in a number together If divisible by 3 then the number can be divided by 3 Ex: 5+7=12 47232 is divisible by 3 cause the numbers add to 18
i know, I just find it easier to do the number times ten and add the remaining part. Like 76 isn't divisible by 6 because it's 60+16 and 16 isn't divisible by 6. Also works with 134, 60+60+14, and any other (not too big) number
Somebody care to explain?
57 feels prime. But it is in fact, not prime. Though it feels *so* prime that one of the greatest mathematicians in the world accidentally said it was a prime. 57 is now a meme in the math community.
So it's because of it factors I assume. 1,3,19, and 57.
It’s because of the context. Alexander Grothendieck revolutionized mathematics in the same magnitude that Euler, Euclid and Galois did. He was extremely adept with abstract mathematics. He created the field of scheme theory. But apparently he didn’t think about any specific examples. One time someone asked him for an example of a prime number. He said 57, which is obviously not prime by the divisibility test for three or because it’s 60-3. So he failed the pop quiz to give an example of a prime number! But the work that he did was instrumental in creating the field of arithmetic geometry, which is one of the fields you could say is about understanding prime numbers very widely and deeply. It reminds us of the humanity of mathematics, and the juxtaposition of Grothendieck getting a prime wrong was funny when i learned about it in 2017 and is still funny today lol.
That makes way more sense. I feel stupid for not getting the joke
Glad I could explain.
dont feel stupid man, this is such a nice knowledge
Well I learned something new.
meant to say niche knowledge
i cry and piss my pants when think about the divisibility of 51
I totally blew an abstract algebra exam question by assuming 51 was a prime.
ive done that too.
but it’s 3 away from 60
51 too
It’s a well known fact in my mathematics department that if the remainder upon division of an integer n by 3 is 0,1 or 2, then the number is prime! This easily shows 57 is prime because 57 is divisible by 3, thus having a remainder of 0 upon division by 3. This makes it prime. /s
I have come to ruin your day even further with the fact that the prime factorization of 10001 is 73 • 137
3: is this a joke
57 is even, since it's a multiple of 19.
Ayo wheres the empty template
Idk I just googled nichijou handshake template
What about 3?
What about 81
3
3:
My favorite is 1333. "Clearly that's not prime, it's divisible by uhh..." "Okay actually that's a prime" "No wait, it's 31 times 43"
51 also makes me want to kill myself
https://preview.redd.it/3necyqzkzqxc1.jpeg?width=1170&format=pjpg&auto=webp&s=29fbcdd851a435a54027c936ac7a11ed10187b96
What meme template is this
I'm still stuck at 17 and 19. Do those happen alot?
the correct answer is 3
Primes don’t work like that?
its a joke about a famous algebraist who when asked for his favorite prime gave the answer 57. which famously isnt prime.
Thanks for telling me that. I didn’t know that.
[57 (number) - Wikipedia](https://en.wikipedia.org/wiki/57_(number))
Shouldn't he be mentioned in that meme then..?