Knowing that predicate $P(x)$ means '$x$ is a prime number' and $a/b$ denotes '$a$ is a divisor of $b$' express the following using logical operators, quantifiers, etc: 'number $z$ is a divisor of the sum of two prime numbers'.
How would I go about doing that? So far I came up with '$z/(P(x) + P(x))$' but honestly that seems too simple to be correct and I'm not sure if I can write the sum of two prime numbers like that.
"The number z is a divisor of the sum of two prime numbers", means: $$\text{There exists two numbers, which are both prime and z is a divisor of their sum.}$$
Is it easier to translate this statement into symbols?
Hint: You were asked to use "logical operators, quantifiers, etc." So can you now see where to do so?