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I'm trying to write the definition of prime numbers using only symbols. Here is what I have: A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers.

Note:

N$^{*}$ is the set of all natural numbers except for $0$.

So the set of prime numbers is S = {x $\in$ N$^{*}$, x $\neq$ 1 $|$ ... [I'm stuck here]}

I don't know how to explain. I was just introduced to proofs and sets so I do not want to use complex symbols. Can someone suggest me a simple way for the "such that" part, please? Thank you!

hanamontana
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$$S = \{ x \in \mathbb{N}, x \neq 1 | \forall p,q \in \mathbb{N},\ pq=x \implies p,q \in \{1, x\} \}$$

John_Krampf
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