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this post was submitted on 21 May 2024
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Yeah, it's not like the mathematics lost any of the numbers. Get your shit together physicists.
I mean mathematicians are still missing over 99.999% of prime numbers, so...
They haven't even found more than two factors, one of which is one, for any prime number, either.
Get it together, Mathematicians.
I think that should be all of them, but if you want to check, there are references on the website where we keep all the numbers detailing how to check any number, or to list all of them if you want an arbitrarily large pile or have infinite time on your hands. :)
Doesn't that miss out n=1?
1 being prime breaks a lot of the useful properties of primes, such as the uniqueness of prime factorization.
Isn't that function listing all the numbers? Not only the primes?
Oh, no that's just the primes. I was responding to a person joking about how we don't even know all the primes, so I used a technical yet unhelpful definition of "the set of all primes" to be technically correct,xas is the mathematics way. :)
I don't know if prime factorization is the correct English word for it but the operation I am referring to takes a (non zero) natural number and returns a multiset of primes that give you the original number when multiplied together. Example:
pf(12)={2,2,3}if we allowed 1 to be a prime then prime factorization cease to be a function aspf(12)={1,2,2,3}andpf(12)={1,1,1,1,2,2,3}become valid solutions.You are correct. The person you're replying to misread my set as a fancy way of saying "all natural numbers", not "all primes".
So you're both right, in that if 1 were a prime, the primes would not work right, and if 1 were not a natural number then those would not work right.
Using the totient function to define the set of primes is admittedly basically just using it for the fancy symbol I'll admit, and the better name for where we keep all the primes is the blackboard bold P. ๐
The technical term you're looking for is "almost all" prime numbers. Not joking btw.
Well they did demonstrate that in a non trivial system of axioms, there will always be true statements that are unprovable. Do they kinda accepted that they will never be able to find everything. https://en.m.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems
Well, either they can't find everything in that system, or they can also find something that contradicts something else that's true.
It balances out, because while there's infinite facts they can't prove, there's also infinite lies they can prove.
show me Pi then
๐ฅง
I know exactly how to find it, and unless you're a mathematician I'm not sure you're authorized to know.
Dunno. Find me an i in the wild.
Whoa there, if you want it's physical location you'll have to ask a physicist, they're in charge of tangible things.
Otherwise, just take a turn perpendicular to the reals, or check in the platonic realm.