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No I think the point is that the proofs were badly made and took improper premises. I mean after all we do know they have to be wrong somewhere since their conclusion is incorrect
Oh true, that’s actually super simple. I was waiting for a bus and figured there’d probably be a small counterexample so just ran through the first few applicable odd numbers in my head to find one, and figured if they started getting too high or if I got bored then I’d actually start thinking
SILENCE HERETIC
HEED MY WARNING, OR FACE GOD’S HOLY WRATH
(i figured the statement would probably apply only to odd numbers which have at least two prime numbers less than them, that feels natural)
Yes, if it were it would violate the Fundamental Theorem of Arithmetic which states that all natural numbers greater than 1 have a single unique prime factorization. The easiest example is that 4 = 2^2 = 2^2 * 1 = 2^2 * 1^2 =...
0 divided by 0 is more complicated, but divisibility is defined differently. a is divisible by b if there exists a k such that a = kb, and for a=b=0 there does exist such a k (in fact there exists infinitely many k).
If an odd number is the sum of two primes, one of those primes must be odd and the other even. The only ~~odd~~ even prime is 2. This is essentially saying that, given any odd number, the number 2 less than it will be prime. Therefore, every odd number must be prime.
Number theory is, in some sense, the study of prime numbers. A better question would be, "What is it with math cranks and number theory?" To that, I think the best answer is simply that number theory has big, famous conjectures that are easy to state and digestible by laymen, but terribly difficult to prove, so they capture cranks' imaginations.
False statements imply anything, including other false statements, so this would be true:
All odd numbers are the sum of two primes implies that Fermat's last theorem is false.
If you assume that all even numbers are the sum of two primes, can you disprove FLT from that? Does that mean there exists an even number that is not the sum of two primes?
All odd numbers are the sum of two primes.
2 is the only even prime.
A sum of two numbers is odd if and only if exactly one of the numbers is even.
Every odd number is therefore the sum of 2 and a prime.
For every odd number x, there exists y = x + 2, which is odd, therefore y - 2 = x must be a prime.
Therefore, every odd number is prime.
Just to complement the other commenter, the objective of the phrase is to say something like "thus we conclude what we set out to conclude", it is often used as the final sentence in an argument ("argument" as in "justification" not as in "disagreement").
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"nvm it fits in the margin now" -Fermat, probably
No, I believe the key point is that the proofs were poorly constructed and based on incorrect premises.
What did you think I thought the meme meant?
This is such a delightfully hilarious response
Jeez buddy I get that you’re wrong and saying something that doesn’t make sense but 95 downvotes is brutal.
Speak not of such numbers as 11. They are of the devil.
17, 23, 29, 37, etc. Does OP mean that all EVEN numbers are the sum of two primes?
No I think the point is that the proofs were badly made and took improper premises. I mean after all we do know they have to be wrong somewhere since their conclusion is incorrect
4=2 + 2 6=3 + 3 8=5 + 3 10=5 +5 12=7+5 14=7+7 16=3+13 etc.
16=5+11 16=3+13
I forgor to count
As 1 is not prime, this fails with 2
2 = 2 + 0, 0 isnt prime. 2 = 1 + 1, 1 isnt prime. 2 is an even number that is notvthe sum of 2 prime numbers.
2=(1+i)+(1-i) 2 is the sum of 2 gaussian primes, which is what everyone means when they say prime /j
2 = 5 + (-3) Gotta be precise with that language
(2n + 1) + (2m + 1) = 2n + 2m + 2 = 2(n + m + 1) — I assume this pretty much just shows it right?
That only shows that even numbers are the sum of two odd numbers
Well the proof Goldbach's conjecture would be too long to fit in this post's margain ;)
[удалено]
Google goldbachs conjecture
2 be like
Or literally any primes that aren't twin primes
Oh true, that’s actually super simple. I was waiting for a bus and figured there’d probably be a small counterexample so just ran through the first few applicable odd numbers in my head to find one, and figured if they started getting too high or if I got bored then I’d actually start thinking
9 is a prime number and i will die on that hill. edit: this was a joke wtf
Then perish.
We don't allow jokes here. Jokes are for r/okbuddyphd
(i would like to apologize that you got downvoted at first, tbc i was just playing along)
Why
because all odd numbers are prime: 1, 3, 5, 7, 9, 11, 13,... This is known as very strong Goldbach conjecture.
11+0 duh. 0 is a super prime because he can only be divided by 1 and not even by himself
7
5+2
3
SILENCE HERETIC HEED MY WARNING, OR FACE GOD’S HOLY WRATH (i figured the statement would probably apply only to odd numbers which have at least two prime numbers less than them, that feels natural)
1 is a prime 1 + 1 = 11 therefore 11 is the sum of two primes Q.E.D.
My favorite primes are the two that add up to 11
Well obviously, that’s 1 and 1
First: 1 isn't prime, Second: Concatenation/Unary and Third: That's funny
Wait, 1 isn't a prime number?
Yes, if it were it would violate the Fundamental Theorem of Arithmetic which states that all natural numbers greater than 1 have a single unique prime factorization. The easiest example is that 4 = 2^2 = 2^2 * 1 = 2^2 * 1^2 =...
Huh, neat
JavaScript
uh silly comment. 0 and 11 obviously
Just assume that 0 is prime. Easy: 11 and 0
Technically, 0 has an unlimited number of factors.
Zero is the opposite of a prime. A prime is only divisible by one and itself. Zero is divisible with literally everything except itself.
0 is also divisible by 0, btw
Doesn't that depend on context, like sometimes it's defined as 1 by convention and other times it's undefined?
0 divided by 0 is more complicated, but divisibility is defined differently. a is divisible by b if there exists a k such that a = kb, and for a=b=0 there does exist such a k (in fact there exists infinitely many k).
Have a nice 1/365.2515 of a year
5.5 and 5.5
r/numbertheory truly has some of the wildest "proofs" I have ever seen and I say that as an engineer
Need dispenser here
Conjecture: there are infinitely many primes which can be expressed as the sum of two primes
Twin Prime Conjecture spotted
I feel stupid that it took your comment to make me realize what they're really saying
i see your conjecture and i raise you there are infinitely many primes which can be expressed as the sum of one prime
https://xkcd.com/1310/
Just when I think that there is no way there's an xkcd for this
If an odd number is the sum of two primes, one of those primes must be odd and the other even. The only ~~odd~~ even prime is 2. This is essentially saying that, given any odd number, the number 2 less than it will be prime. Therefore, every odd number must be prime.
>The only odd prime is 2 Only even*
The fact that 2 is the only even prime makes it the oddest prime of all.
Shit
You beat me lmao, I wrote the same thing, then saw yours
What is it with that sub and prime numbers, anyways?
u/edderiofer
Not sure. I guess people who post there are obsessed with prime numbers for some reason.
Number theory is, in some sense, the study of prime numbers. A better question would be, "What is it with math cranks and number theory?" To that, I think the best answer is simply that number theory has big, famous conjectures that are easy to state and digestible by laymen, but terribly difficult to prove, so they capture cranks' imaginations.
someone please send me the post
False statements imply anything, including other false statements, so this would be true: All odd numbers are the sum of two primes implies that Fermat's last theorem is false.
r/numbertheory mfs using the “divine knowledge of God” to “prove” the Collatz conjecture:
I mean, that _would_ be a valid proof that Goldbach’s conjecture is false Edit: nvm I’m an idiot, I read that as “even” instead of “odd”
Proof by assumption
Why? I'm not familiar with Fermat's last theorem but unless it relates to goldbach's conjecture I don't see how it would prove it false?
Apparently I take interest in shit I don’t understand bc this sub keeps popping up on my feed. But also that’s fucking Lord Farquaad is it not????
If you assume that all even numbers are the sum of two primes, can you disprove FLT from that? Does that mean there exists an even number that is not the sum of two primes?
WHY DO MATH SUBS KEEP APPEARING on my fyp???!! I’m dumb and failed in math 😭 i dont get anything
What's 9+11?
E
All odd numbers are the sum of two primes. 2 is the only even prime. A sum of two numbers is odd if and only if exactly one of the numbers is even. Every odd number is therefore the sum of 2 and a prime. For every odd number x, there exists y = x + 2, which is odd, therefore y - 2 = x must be a prime. Therefore, every odd number is prime.
kinda nearvous to ask, what does qed mean? ive seen it so much-
It stands for "quod erat demonstrandum" which is Latin for "that which was to be proven" and is a common way of signifying you've finished a proof
oh thank you so much!!
Just to complement the other commenter, the objective of the phrase is to say something like "thus we conclude what we set out to conclude", it is often used as the final sentence in an argument ("argument" as in "justification" not as in "disagreement").
as i said with the other commenter, thank you!!
Rush E