Is the number 1 a prime number?

One is not a prime number

In most cases it doesn't really matter whether it counts as a prime or not, so many people who have only done relatively basic math think it is, and they have never needed to be corrected.

However in a number of situations it does matter - and people who have done maths to this advanced level will have learned that one is not a prime number.

I found this page which sets out a number of these reasons.

In mathematics, a prime number (or a prime) is a natural number which has exactly two distinct natural number divisors: 1 and itself. An infinitude of prime numbers exists, as demonstrated by Euclid in about 300 BC. The first thirty prime numbers are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113

NO The first thirty prime numbers are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113

from most prime number definition..'In mathematics, a prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself'

and example of natural numbers (1,2,3,4,5........)

from the above definitions, then 1 is not a prime number because it does not have two distinct natural number divisors.

the key word here is 'two distinct ..divisor' although some believe it is a prime number as it have two divisor 1 and itself which is also 1. but that goes against the definition.

have a nice day (it is a prime number.....)

A prime number is a number which can only be divided by itself and 1,

and because in the case of 1, itself and 1 are the same thing, technically it is not a prime number.

So, 2 is the first prime number.

Mathematicians want to be able to factor any positive integer into powers of postive prime numbers uniquely. For example, 12 is uniquely factorized into 2^2 * 3, and 3,528 is uniquely factorized into 2^3 * 3^2 * 7^2. Now, if we say that 1 is a prime number, then we'd have 12 = 1^a * 2^2 * 3, and 3,528 = 1^b * 2^3 * 3^2 * 7^2, where a and b are any positive integer, which means such factorization is not unique. That's why by convention 1 is not called a prime number.

Addendum: Thanks P P, for citing a paper that supports what I said.

No, because a prime number has two factors: 1, and itself. But for this number, it only has one factor: 1.

Two IS a prime number, since it has 2 factors, 1 and 2. Hope this helps!

No. The defn of a prime number is one that has TWO factors which are integers. These factors are 1 and itself. 1 only has one factor and that is 1.

1 is not a prime number beacuse prime numbers are natural numbers greater than 1 whose only divisors among the natural numbers are 1 and themselves

No, it has 2 factors, although the second is not widely recognises. There is of course 1. But also there is 0.

Let me explain. 5^0=1 8^0=1 2,543,722^0=1.

Anything to the power of 0 is 1. Therefore 0^0=1, making 0 a factor of 1, therefore giving it 2 factors. This is a grey area in maths, but it does work.