TITLE: What is the standard notation to represent the set of primes?
QUESTION [13 upvotes]: I have seen $\mathbb Z_p$. Are there others, perhaps $\mathbb N_p$?
or the set of natural numbers where the totient of $ n $ equal $ n - 1 $ ?
$$ \{n \in \mathbb N \mid n\ge2,\phi (n) = n-1\}$$

REPLY [3 votes]: IF we use  $\mathbb P$, we have to clarify that it shall be the set of Primes like this:
$\mathbb P = \{ p \in \mathbb N \; | \; \text{p is prime}\}$.
As far as I know there is no official definition for the set of primes.
Mostly seen in my literature is e.g. Let a $\in \mathbb C$, let p be prime.
Source: I'm studying math @ Free University of Berlin.