I need help with notation for a finite set of random primes.
Edit I've inserted my take on the format from the answer. Does it work?
My attempt:$$\{X\in\binom{\mathbf P_{3,100}}{20}\},$$
$$\{p_{i}\in\textbf{P}: 3\leq i \leq 100 \land \text{#}=20\text{ (at random)}\},$$where I want the range $p_{3}$ to $p_{100}$ and I want 20 primes.
$$\{X\in\binom{\mathbf P}{20}\},$$$$\{p_{i}\in\textbf{P}: 1\leq i\land\text{#}=20\text{ (at random)}\},$$where I want 20 primes.
Is there a better way to show this?
If I had encountered this set, I would not know what it means.
Instead, write $\mathbf P_{n,m}$ for the set $\{p_n,\ldots,p_m\}$. Now we can say that $X\subseteq\mathbf P_{3,100}$ and $|X|=20$, or $X\in\binom{\mathbf P_{3,100}}{20}$.
Since we didn't specify what are the elements of $X$, they are arbitrary (or "random" if you prefer to stick to that term).
Or if you dislike that, you write say that $i_1,\ldots,i_{20}$ are arbitrary integers between $3$ and $100$, and then consider $\{p_{i_j}\mid 1\leq j\leq 20\}$.