# Divisible by a prime number 2, or by the prime number 2

I want to state that "the integer 4 is divisible by a/the prime number 2."

Which is correct a or the?

Since 2 is a specific number, so "the" may be ok. But if I want to use "a prime number" as adjective, maybe "a" is ok.

Also I would like to know whether "by prime 2" is correct or not.

The way we would usually say it is

It is divisible by the prime number 2.

You use the definite article because it's a specific, known prime number. "Prime" is the adjective modifying "number 2", the noun.

It is divisible by a prime number.

Means it is divisible by some unspecified prime number (or numbers).

"Prime 2" is not normally used (although it could be the name of a character in a science fiction movie).

The correct form is:

The integer 4 is divisible by the prime number 2.

This is because there is only one prime number with the value 2.

You can also say

The integer 4 is divisible by a prime number.

This statement indicates that 4 is a multiple of a prime number without saying which one.

Because you are specifically mentioning the number "2" it is

Divisible by the prime number 2.
divisible by the number 2