What is the symbol for primes?

Although there isn't much difference between $\mathbb{Z},\mathbb{N},\mathbb{I}$, they are well-known, and each one gets its own distinguished symbol. Is there any reason that primes don't get their own special symbol? Or is there an already commonly used symbol for primes?

Solution 1:

Relevant / duplicate / posted on MO: A symbol to denote the set of prime numbers.

From the thread on MO, and from what I've seen elsewhere, the symbol $$ \Huge\mathbb{P} $$ is sometimes used. This doesn't really seem to be all too common though (not universal anyway).

Solution 2:

Whatever you go with, remember that $\mathbb{P}$ is commonly used elsewhere, so make it very clear in your writing that you're defining it to be the set of primes. Personally, I've never seen $\mathbb{P}$ used to denote the primes, although apparently some do.

For example, although the expression $\displaystyle \sum_{p \in \mathbb{P}} \frac{1}{p} = \infty$ has an appealing brevity to it, I've grown to just bite the bullet and write $\displaystyle \sum_{p\text{ prime} } \frac{1}{p} = \infty$. I will concede that, given their importance, the primes not having a widely agreed-upon symbol is one of the major notational shortcomings of modern mathematics.