Is 1 a prime number?

[Darth_Ole]

When you're young you're taught that 1 is not neither prime nor composite. But I've argued with people that 1 is in fact prime because it only has two factors: 1 and itself.

Any of you know?

[FlashHarry]

1. Well...

...if a prime number is a number that is only divisible by 1 and itself... then, I guess it is a prime number.

[Susang]

2. 1 is the lonelist number

Other than that, I have no idea. :-)

[unblock]

3. 1 is not considered a prime number

[Ivory_Tower]

4. I've seen definitions of prime

That say "a number greater than one is prime if...."

So by that definition I would say no. (Most lists of primes start with 2.) (Edit: All lists of primes?)

[DemoVet]

8. Which is the only even prime number!

[boxster]

15. 2

Yep, 2's the only one! No pun intended.

[TheZoo]

5. No

The definition of a prime number is: An integer greater than one is called a prime number if its only positive divisors (factors) are one and itself.

The Fundamental Theorem of Arithmetic states that "Every positive integer greater than one can be written uniquely as a product of primes, with the prime factors in the product written in order of nondecreasing size."

So, while "One is a Lonely Number", it's not a Prime number.

On edit: Thanks for this topic! I've started reading a lot on Prime Numbers and Math in general on my breaks at work.

[unblock]

6. the main reason 1 is not considered a prime number

is so that all numbers have a unique prime factorization.

e.g., the prime factors of 15 are 3 and 5. if 1 were considered prime, then the prime factors of 15 could be 5, 3, and 1. or 5, 3, 1, and 1. you get the idea.

[yankeeinlouisiana]

7. I'll ask my son

in the morning. He's sleeping now. He's good at math and he's at the right age for this question. I don't remember if it is or isn't. It seems to fall into that category, but...:shrug:

[Superfly]

9. Is 0 a prime number?

Since the definition of a prime number is any number than can be divisible only by 1 and itself, is 0 a prime number?

0/1 = 0

0/0 = undefined or 1

[punpirate]

10. Nope...

... dividing by zero is an illegal function, mostly because it signifies an unquantifiable result.

Cheers.

[Superfly]

11. Yeah, but what is

0/0? Zero goes into zero exactly 1 or an infinite number of times. Now I remember why I haven't used math since learning difficult (differential) equations.

[Superfly]

12. Answered my own question

"Zero is not a prime or a composite number either. Zero has an infinite
number of divisors (any nonzero whole number divides zero). It cannot
be written as a product of two factors, neither of which is itself, so
zero is also not composite. It falls in a class of numbers called
zero-divisors. These are numbers such that, when multiplied by some
nonzero number, the product is zero."

[Akbar]

13. 0/0 is Undefined

If one accepts that 0/0 is 1, then all numbers are equal.

[Shakeydave]

14. Arrrrrrrrrrrrrrrrrrggggggggggghhhhhh!

I'm back in Mrs. Brierly's 4th grade math! Don't send me there! :freak: