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/sci/ - Science & Math

Why is 1 not prime?
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>>12939311
A number is "prime" when it can be divided by exactly 2 distinct numbers
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>>12939311
because "prime number" is shorter than "prime number greater than 1"
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>>12939311
How 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
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>>12939315
says who?
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>>12939311
1 isn't even a number, it generates numbers. why would it be prime?
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>>12939311
Because I say so
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>>12939324
Everyone
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>>12939351
>1 isn't a number
next thing your gonna tell me is that atoms aren't matter
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>>12939364
wrong
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>>12939311
It is. 1 is divisible by only 1 and itself.
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>>12939366
atoms aren't matter, it's a model of matter.
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>>12939381
Matter doesn't even exist, that's just a concept you came up with, you can't prove it actually exists.
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>>12939366
atoms don't generate matter
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>>12939396
atoms compose matter
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>>12939311
Because it's a square number
Prime numbers cannot be square numbers
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>>12939311
Purely convention
If 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.
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>>12939430
that makes two reasons why the atoms analogy fails
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>>12939386
do you have senses?
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i know why
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Because then every number will have infinity of prime divisors.
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>>12939445
Surprised there's no equivalent for "where (denominators)=/= 0" given that division by 0 is far more obtrusive.
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>>12939510
No, why, do you think that you do have senses?
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>>12939615
because of my senses
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>>12939639
Define senses.
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>>12939663
organs which I can use to detect and observe the environment that surrounds me
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>>12939734
And you trust these strange 'organs' you have? Dunno, sounds weird to me!
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btw it seems fucking unreal that there is infinite number of prime numbers
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>>12939324
I do
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>>12939755
Sure
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>>12939760
I'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!
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>>12939311
>Why is 1 not prime?

Go ahead a define it as prime... it will not change anything
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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
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>>12940028
Except the fundamental theorem of arithmetic.
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>>12940067
1 <
here i fixed fta for you
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>>12940067

Depressing that the real answer took this long.
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>>12940664
that's not a real answer, you can literally just add 1 < to any standard statement of fta
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>>12940715

By 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.
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>>12940028
almost every statement involving prime numbers will become false
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>>12940751
for 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.
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>>12939386
4channel doesn’t exist so stop posting
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>>12939311
Because including the multiplicative identity is trivial when factorization of integers is our concern.
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>>12939311
>>12940872
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>>12939315
1 and -1 both divide 1 while no other number does. Therefore, 1 is prime.
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>>12939375
sorry, he meant everyone who has an opinion on anything concerning mathematics that matters
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>>12940916
>-1
>natural number
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>>12941033
Who said anything about natural numbers?
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>>12939311
https://ncatlab.org/nlab/show/too+simple+to+be+simple
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>>12939377
>and
That's not what and means, dipshit. >>12939386
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Primes have two and only two integer divisors.
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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
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>>12939324
thats how p is defined
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>>12943412
retard
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>>12939311
Is Infinity prime?
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>>12943143
Mathematicians.
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>>12943771
https://en.wikipedia.org/wiki/Supernatural_number
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>>12943779
So you're admitting that a prime number doesn't have exactly two divisors?
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>>12939311
Prime numbers are the atoms of the divisibility lattice.

https://en.wikipedia.org/wiki/Division_lattice
https://en.wikipedia.org/wiki/Atom_(order_theory)
https://ncatlab.org/nlab/show/atom
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>>12943903
No I said mathematicians said things about natural numbers.
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>>12939311
1 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.
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>>12939311
1 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
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>>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".

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