Does this qualify as a statement?

Question

Is this a statement?

All positive integers with negative squares are prime.

What do we need to qualify as such?

Answer 1

Yes it is a statement. It may sound absurd, but it is a statement, and it happens to be vacuously true.

However, a statement doesn't have to be true: logically, a statement, sometimes called a proposition, is an assertion that can be assessed as either true, or else false, and cannot be both true and false. We do not necessarily need to know at a given point in time exactly what its truth value is, but it simply needs to be such that it is true or else false.

Examples of non-statements:

• How are you?
• Do your homework!

ADDED: see vacuous truth.

A vacuous truth is a truth that is devoid of content because it asserts something about all members of a class that is empty or because it says “If A then B” when in fact A is inherently false.

Answer 2

A statement needs to have the property of being true or false. "The best integers are prime" is not a statement, but an opinion. The one in OP is indeed a statement, and is also true.