Question: Is This a Proposition?

Question

Every positive even integer can be written as the sum of two primes.

The answer is: this is a proposition. Nobody knows its truth value, but it's unique.

I wonder what is unique and why its uniqueness makes this statement a proposition.

Answer 1

The term unique is misused here. I'm not certain what term would be the best, but they are trying to convey the following : "the proposition is either true or false, it cannot be both".

A proposition must have a truth value. The proposition showed definitely has a truth value, while we don't know which one, it doesn't change the fact that it has one. Therefore it is a proposition

Answer 2

Every even integer greater than $~2~$ can be expressed as the sum of two primes.

This is called Goldbach's conjecture which is one of the oldest and best-known unsolved problems in number theory and all of mathematics.

The conjecture has been shown to hold for all integers less than $~4 × 10^{18}~$, but remains unproven despite considerable effort.

Note: In mathematics, a conjecture is a conclusion or proposition based on incomplete information, for which no proof or disproof has yet been found.

So you can conclude that this statement is a proposition.

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From Wikipedia