2 may be the only even prime - that is it's the only prime divisible by 2 - but 3 is the only prime divisible by 3 and 5 is the only prime divisible by 5, so I fail to see how this is unique.
Exactly, "even" litterally means divisible by 2. We could easily come up with a term for divisible by 3 or 5. Maybe there even is one. So yeah 2 is nothing special.
"Threven" has a nice ring to it now that I think of it.
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Gtfo! 😅
2 is a prime though isn't it
Yes, but it's the only even one. Making him the odd man out
It is but if feels wrong
It pretends to be prime and we all go along with it to avoid hurting its feeling.
Even vs odd numbers are not as important as we think they are. We could do the same to any other prime number. 2 is the only even prime (meaning it is divisible by 2) 3 is the only number divisible by 3. 5 is the only prime divisible by 5. When you think about the definition of prime numbers, this is a trivial conclusion.
Tldr: be mindful of your conventions.
Yes, but not really.
With 2, the natural numbers divide into equal halves. One of which we call odd and the other even. And we use this property a lot in math.
If you do it with 3, then one group is going to be a third and the other two thirds (ignore that both sets are infinite, you may assume a continuous finite subset of the natural numbers for this argument).
And this imbalance only gets worse with bigger primes.
So yes, 2 is special. It is the first and smallest prime and it is the number that primarily underlies concepts such as balance, symmetry, duplication and equality.
But why would you divide the numbers to two sets? It is reasonable for when considering 2, but if you really want to generalize, for 3 you’d need to divide the numbers to three sets. One that divide by 3, one that has remainder of 1 and one that has remainder of 2. This way you have 3 symmetric sets of numbers and you can give them special names and find their special properties and assign importance to them. This can also be done for 5 with 5 symmetric sets, 7, 11, and any other prime number.
Then you have one set that contains multiples of 3 and two sets that do not, so it is not symmetric.
You'd have one set that are multiples of 3, one set that are multiples of 3 plus 1, and one stat that are multiples of 3 minus 1 (or plus 2)
Not sure about how relevant this in reality, but when it comes to alternating series, this might be relevant. For example the Fourier series expansion of cosine and other trig function?
But then it is more natural to use the complex version of the Fourier series, which has a neat symmetric notation
I don’t know if it’s intentional or not, but you’re describing cyclical groups
The meme works better if it's 1 instead of 2. 1 is mostly not considered a prime number because a bunch of theorems like the fundamental theorem of arithmetic would have to be reworked to say "prime numbers greater than 1." However, just because 1 is not a prime number doesn't mean it's a composite number, so 1 is a number that is neither prime nor composite.
2 is a prime number, but shit ton of theorems only apply to odd prime numbers, and a lot of other theorems treat 2 as a special separate case, because it behaves weirdly.
I don't get it, why does adding a hand move to the next prime?
🚨 NERD ALERT🚨
Go define a vector space, nerd.
Go compute the p value of you being cool
Go integrate f(x)= 1/x on the domain (-1,1)
This is meme-ville population: me
Take a hike.
Spoiler: p < 0.05
what why i'm serious i don't get why the hands decrement the numbers
I'm picking on you because you're looking for patterns where there are none. It's a common meme format, and it just so happens that op wrote it like that.
Was trying for absurd. Didn't mean to offend
what I don't get is what the meme format's supposed to mean, I can't even find the name of it online
let V be you mom’s vagina, a vector space over the field of pubes. We define my d as a vector such that d is in V. Thus my dick is in your mom’s vagina.
In this vector space p values are not defined, but I can assure you that my pp is > 9000.
The integral of f(x)=1/x from -1 to 1 does not converge, just like how your father is never coming back from from buying milk. The principal value of that integral tho is 0, just like the amount of hugs you got as a kid.
math is cool, you just too stupid to get it.
Pretty sure that when we plug in a correction factor for the relative age of the Fediverse userbase, "today's lucky 10,000" becomes more like "today's lucky 10 million"
It's just the way the power rangers combined their forces
Oh yeah? What about 0? And 1?
They're not prime.
Commonly primes are defined as natural numbers greater than 1 that have only trivial divisors. Your definition kinda works, but 1 can be infinitely many prime factors since every number has 1^n with n ∈ ℕ as a prime factor. And your definition is kinda misleading when generalising primes.
Isn't 1^n just 1? As in not a new number. I'd argue that 1*1==1*1*1. They're not some subtly different ones. I agree that the concept of primes only becomes useful for natural numbers >1.
How is my definition misleading?
It is no new number, though you can add infinitely many ones to the prime factorisation if you want to. In general we don't append 1 to the prime factorisation because it is trivial.
In commutative Algebra, a unitary commutative ring can have multiple units (in the multiplicative group of the reals only 1 is a unit, x*1=x, in this ring you have several "ones"). There are elemrnts in these rings which we call prime, because their prime factorisation only contains trivial prime factors, but of course all units of said ring are prime factors. Hence it is a bit quirky to define ordinary primes they way you did, it is not about the amount of prime factors, it is about their properties.
Edit: also important to know: (ℝ,×), the multiplicative goup of the reals, is a commutative, unitary ring, which happens to have only one unit, so our ordinary primes are a special case of the general prime elements.
Oof, I remember why I didn't study math 😅
But thanks for the explanation
There is multiple things wrong here.
1 is not a prime number because it is a unit and hence by definition excluded from being a prime.
You probably don't mean units but identity elements:
There are more units in R than just 1, take for example -1(unless your ring has characteristic 2 in which case thi argument not always works; however for the case of real numbers this is not relevant). But there is always just one identity element, so there is at most one "1" in any ring. Indeed suppose you have two identities e,f. Then e = ef = f because e,f both are identities.
The property "their prime factorisaton only contains trivial prime factors" is a circular definition as this requires knowledge about "being prime". A prime (in Z) is normally defined as an irreducible element, i.e. p is a prime number if p=ab implies that either a or b is a unit (which is exactly the property of only having the factors 1 and p itself (up to a unit)).
(R,×) is not a ring (at least not in a way I am aware of) and not even a group (unless you exclude 0).
What are those "general prime elements"? Do you mean prime elements in a ring (or irreducible elements?)? Or something completely different?
0 has all the factors. Itself and any other number.
Put them in a sieve of Eratosthenes and see what happens.
Spoiler, they aren't.
Yo what about my man 9
7 ate them
9 isnt prime, it's divisible by 7
just not very well...
Two is the oddest prime of them all.
