A number that is even and prime. So I have the following sentence : There exists a unique prime number that is even.

I have the following predicates :

Prim(x) : x is a prime number.
Even(x) : x is an even number.

My answer : Prim(Even(x))

I don't know, but I think that this would be better : Ǝ Prim(Even(x))

Would this make sense ? Even though we know that there is only one such number that is prime and even.

Thank yoU!
"There is exactly one even prime number" can be expressed formally as
$$ \exists x: [(Even(x) \land Prim(x)) \land \forall y : [Even(y) \land Prim(y) \implies x=y]]. $$
The first part says there is at least one even prime number. The second part says there is at most one even prime number.
For the statement &quot;There exists a unique Prime number that is Even.&quot;
it's rather more simple.
$\exists  x: [\operatorname{Even}(x)\land\operatorname{Prim}(x)]$
My explanation for this is that the existential quantifier $\exists x$  means:-

There exists an 'x'
For some 'x'
For at least one 'x'

Here it is used to reference that &quot;there exists a unique 'x' satisfying both $\operatorname{Even}(x)$ and $\operatorname{Prim}(x)$&quot;.