prime numbers?

Question

can any body tell me why the number 1 is not a prime number, the thing that defines a prime number is that is only devisable by itself, and the number 1.

now the number 1 conforms to both these points, so why is it not classed as a prime number ?

Answer 1

In it's simplest terms a prime number is one which has exactly 2 factors - 1 and itself.

1 does not have 2 factors and is therefore not prime.

K x

Answer 2

Because that is not the full definition. Primes are defined on numbers greater than 1. 1 is specifically excluded.
Why is it excluded? If it is included, Number Theory doesn't add up!
Every number is divisible by 1, every prime factorisation would contain 1, these results are trivial and unproductive, the discipline works because we exclude 1. This is because 1 is the identity under multiplication

Answer 3

They choose to define a 'prime number' in a particular way. And that definition does not include 1. It could have. But they choose not to include it.
Now, you are asking why.? Well, i think because the whole purpose of identifying prime numbers was to know which numbers among natural numbers cant be built by anything other than 1.
Think of it this way. Every number can be thought of as a building block. Like in a LEGO set. Now, 1 is the most basic building block. Its obvious u can build everything (all natural numbers) using 1. Now u ask urself, if i choose not build some number using 1, then can i build it using building blocks some other number in such a way that u use only blocks of that number and no other blocks? If u choose say 6, u can use the building block '2' three times to build 6. Or u can use the building block '3' two times to build 6. Also u need to know how many types of building blocks other than 1 can be used to build it. And in the case of 6, u know they are two types, '2' and '3'.
But what about 7 ? You realise, that if u choose not to build it using 1, then u have no option but get the whole of 7. You cant build it. So 7 is a number which refuses to be built by anything other than 1. Now, numbers like 7 and 5 can be used to build other numbers. Thus saving u the trouble of having to build them using 1. But they themselves cant be built except by 1. So u can either build them using 1 or just get a whole building block.
Now our whole purpose of defining this concept is to identify such numbers. So whats the use of including one among them?

Answer 4

I think because while 1 can be divised into 1x1 (fitting your comments) 1 can also equal 1 x 1 x 1 or 1 x 1 x 1 x 1..... ad infinitum. Thus technically, 1 is NOT only divisable by itself and the number 1 unlike say 17 which can only be 17 x 1.

Answer 5

In mathematics, a prime number (or prime) is a natural number greater than one whose only positive divisors are one and itself. A natural number that is greater than one and is not a prime is called a composite number. The numbers zero and one are neither prime nor composite. The property of being a prime is called primality. Prime numbers are of fundamental importance in number theory.

Answer 6

A number is prime if it has two 'distinct' factors (or divisors), itself and 1. (See wiki definition)

Distinct means different.

The 2 factors of 1 are '1' and '1'.

1 and 1 are not different, therefore 1 is not prime.

QED

Answer 7

It is just becuase the second rule trumps the first and the number itself is 1 so it would defeat the purpose of multiplying 1 by itself to get the exact same answer.

Answer 8

One is most certainly a prime number, but sine it is divisible into any other number, most mathematicians do not include as a prime number, 'non-trivial factor'.
(Riemann's Hypothesis and the prime number theorem will shed more light on the subject)

Answer 9

one is not a prime number because of two reasons
1. there are no two numbers that can divide it exactly, there is oly one)
2.1 is the number that has 3 roots, 2 complex and 1 real

Answer 10

The change in label occurred so that it can be said 'each number has a unique factorization into primes.'