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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.

Please give me some advice.

3 Answers 3

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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).

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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.

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

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

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