Why is 1 not prime?
>>12939311A number is "prime" when it can be divided by exactly 2 distinct numbers
>>12939311because "prime number" is shorter than "prime number greater than 1"
>>12939311How can it be prime when primes don't actually exist? Your definition of a prime doesn't prove they actually exist you know!t. free-thinker expert
>>129393111 isn't even a number, it generates numbers. why would it be prime?
>>12939311Because I say so
>>12939351>1 isn't a numbernext thing your gonna tell me is that atoms aren't matter
>>12939311It is. 1 is divisible by only 1 and itself.
>>12939366atoms aren't matter, it's a model of matter.
>>12939381Matter doesn't even exist, that's just a concept you came up with, you can't prove it actually exists.
>>12939366atoms don't generate matter
>>12939396atoms compose matter
>>12939311Because it's a square numberPrime numbers cannot be square numbers
>>12939311Purely conventionIf you included 1 in the set of primes then there would be a lot of theorems that would be reworded to say "for all primes except 1". In comparaison the judgement "x is a prime or 1" is practically never used with current mathematics, so we chose the most convenient option.Everything in maths is arbitrary definitions stacked on top of each other, the point is to chose the ones that can model whatever you want to work on.
>>12939430that makes two reasons why the atoms analogy fails
>>12939386do you have senses?
i know why
Because then every number will have infinity of prime divisors.
>>12939445Surprised there's no equivalent for "where (denominators)=/= 0" given that division by 0 is far more obtrusive.
>>12939510No, why, do you think that you do have senses?
>>12939615because of my senses
>>12939663organs which I can use to detect and observe the environment that surrounds me
>>12939734And you trust these strange 'organs' you have? Dunno, sounds weird to me!
btw it seems fucking unreal that there is infinite number of prime numbers
>>12939760I've already pointed out, since I'm so brilliant and all, that just because you've defined a prime number doesn't mean it exists! Ha! Keep doing your fake math like you have been the past 100 years, you'll never be as smart as me since I question everything!
>>12939311>Why is 1 not prime?Go ahead a define it as prime... it will not change anything
Becouse of the uniqueness of prime factorization.If 1 would be preime, then faggots would say, heh 1 times the number is that numbers too yaaaaaaaaaaaas queeeeeeeeeen
>>12940028Except the fundamental theorem of arithmetic.
>>129400671 < here i fixed fta for you
>>12940067Depressing that the real answer took this long.
>>12940664that's not a real answer, you can literally just add 1 < to any standard statement of fta
>>12940715By this poorly described notion I assume you mean "all primes greater than one" (where one is admitted as prime) or similar caveat language, in which case the statement of the theorem is made less elegant so yes, it is a real answer.
>>12940028almost every statement involving prime numbers will become false
>>12940751for example, take the crandall & pomerance statement of fta:for each natural number n there is a unique factorization n = (p^a_1)(p^a_2)...(p^a_k) where exponents a_i are positive integers and [ 1 < ] p_1 < p_2 < ... < p_k are primes.
>>129393864channel doesn’t exist so stop posting
>>12939311Because including the multiplicative identity is trivial when factorization of integers is our concern.
>>129393151 and -1 both divide 1 while no other number does. Therefore, 1 is prime.
>>12939375sorry, he meant everyone who has an opinion on anything concerning mathematics that matters
>>12941033Who said anything about natural numbers?
>>12939377>andThat's not what and means, dipshit. >>12939386
Primes have two and only two integer divisors.
bc if you make a division by primes, you will ever get times one, so this would make the factorization not unique, and it's just awful, like the other one said about being convenient
>>12939324thats how p is defined
>>12939311Is Infinity prime?
>>12943779So you're admitting that a prime number doesn't have exactly two divisors?
>>12939311Prime numbers are the atoms of the divisibility lattice.https://en.wikipedia.org/wiki/Division_latticehttps://en.wikipedia.org/wiki/Atom_(order_theory)https://ncatlab.org/nlab/show/atom
>>12943903No I said mathematicians said things about natural numbers.
>>129393111 is the most primary prime number of all.Think about it all numbers are primary based one 1. Every number can be divided by 1. Every number can be broken down in 1s. Thats how primary it is its father and mother of all numbers ever.
>>129393111 is non-prime because Gauss said so. His reasoning seemed pretty solid to me when I read it, but the true fundamental reason why 1 is defined as non-prime is that Gauss said so and nobody of equal stature has ever come along to refute it
>>12939386>what is matter?matter is composed of "atoms"we assume "atoms" to be....the smallest divisible units of elements....breaking down beyond this "atom" unit will result in losing that elements chemical properties.so, matter is what we term "the elements" and are composed of "atoms" that will lose their unique chemical properties if broken down any further.NB: all other mass, etc is classified as a particles under "particle-physics".