Why $ 2$ is a prime number since it has different representation than other primes?

Question

it is well known that the integer $2$ is a prime number as it satsfying the definition of prime number , Another remark is that the presentation of the integer 2 is different from others primes , for example (it is the product of even integer times $1$ ($2=2\times 1$ ) but others primes are the products of odd integers times 1 , Then my question here is : Why $2$ is a prime number however it has differents representation than other odd primes ?

Note: Probably the unit integer which it is 1 excluded from the list of primes as a reason it's representation as the product of the number times it self ($1=1\times 1$)which it is different from other primes representation

Answer 1

Note that

• $1$ is to be excluded since every integer number is multiple of $1$
• $2$ is included since it is the "first even" number; it is true that the others primes are odd (i.e. not multiple of 2) but this holds because the key property is that primes are not multiple of the previuos numbers other than 1.