Is 1 a Prime Number?

A long time ago, it was considered to be prime. But prime numbers have a lot of very interesting properties that 1 does not have, so the definition has been narrowed to exclude it. The correct definition is:

Prime numbers are natural numbers > 1 that have exactly 2 factors (1 and themselves). https://en.wikipedia.org/wiki/Prime_number#Primali... discusses this history and the reason 1 is no longer considered prime. If 1 were included in the primes, hundreds of theorems would have to read "Let p be a prime other than 1." It's better to just exclude it.

It's all about definitions. It's not about proving whether 1 is prime or not. Mathematicians now agree that it's better (more convenient) to simply say 1 is not a prime. The simplest reason that 1 is not a prime is because today's definition says that it's not.

No 1 is not a prime number

No.

A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.

The fundamental theorem of arithmetic establishes the central role of primes in number theory: any integer greater than 1 can be expressed as a product of primes that is unique up to ordering. The uniqueness in this theorem requires excluding 1 as a prime because one can include arbitrarily many instances of 1 in any factorization, e.g., 3, 1 · 3, 1 · 1 · 3, etc. are all valid factorizations of 3.

No. Prime numbers are defined to exclude 1.

Why? Any number can be multiplied by 1 any number of times without changing the result.

If 1 was prime, you could factor 2 in multiple ways:

2

2x1

1x2

2x1x1

and so on.

This renders unique factorization (aka the fundamental theorem of arithmetic) impossible. Therefore 1 is defined as not prime.

No. 1 is not a Prime Number.

A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number.

No. The definition of a prime number is a number that only has itself and 1 as a factor: 2 factors.

1 only has 1 factor, so is neither prime nor composite.

No. It is not a prime number by definition because it is not a building block of non-primes. you never include 1 when asked for the prime factors of a number. If you did, you would always have an extra 1 to write at the beginning which just isn't nice.

no 1 is not a prime number.

No it's not, a prime number is where you only have 2 factoids, 1 only has itself as a factor.

For some unknown reason 1 is not prime, but for another unknown reason 2 is. Doesn't it seem as if it should be the other way around, really?