Is 1 a prime number or not ?

>>9101656
Depends. When you write your book on number theory do you want to waste more ink in every theorem by stating "except for 1" after making any claim of the form "show that for every prime"? No right? Good.

>>9101656
a prime number is defined as one that has only two whole number factors: the number itself, and one.

Since the only whole number factor of 1 is itself, it does not meet the condition of a prime number.

1 is not a number.

>>9101663
>a prime number is defined as one that has only two whole number factors: the number itself, and one.
1 = 1.1, i don't see where it contradicts the definition

>>9101663
Err, it doesn't contradict anything.

>>9101656
Number theorists on suicidewatch

>>9101720
Does 1.1 look like a whole number, to you? Fucking retard, get with the game

>>9101724
Sure it does, 1 only has one whole-number factor.

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>>9101741
>Does 1.1 look like a whole number, to you?

It could be prime, but mathematicians have decided it shouldn't be because it's comfy that there's only one way to represent composite numbers as a product of primes. If one was prime there would be an infinite number of ways to represent composite numbers as a product of primes.

>>9101720
1 still only has one factor, and thus it cannot be prime

>>9101741
Senpai

1. A number must be divisible only by itself
1/1 = 1

2. And it must be divisible by 1
1/1 = 1

Both conditions are met.
The reason we exclude it is because whenever you talk about prime numbers you have to exclude 1 in theorems. That's literally the only reason.

>>9102035
it's really just so it follows the fundamental theorem of arithmetic

>>9101656

If it is regarded as being prime, then this breaks the present statement of FTArith. Since we don't want this, and since 1 is, when you get right down to it, a very-extra-special number, we say that 1 is not prime.

>>9101664
underrated

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56KB, 400x267px

>>9101656
moreover, -1 is prime

>>9101656
1 is the loneliest number that you'll ever do.

>>9102084
2 can be as bad as 1

>>9101663
>a prime number is a whole number having exactly two distinct whole number factors
FTFY