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.
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.
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?
Then you have one set that contains multiples of 3 and two sets that do not, so it is not symmetric.
I don’t know if it’s intentional or not, but you’re describing cyclical groups
2 is a prime though isn’t it
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.
Two is the oddest prime of them all.
