Notation For the $n$th Prime

Question

What is the standard notation for the $n$th prime? How would I notate the prime that is $n$ more or less than the $n$th prime?

I have seen notation for the $n$th prime on various webpages, but I am not so clear on how to type it or how to use it in mathematical expressions and operations.

Answer 1

There is no universal standard notation, but it is not uncommon to see $p_1, p_2, p_3,\ldots $ to denote the first, second, third primes (respectively). In MathJax and LaTeX this is typeset as p_n for the subscript. To write that a prime is $n$ more than the $n^\textrm{th}$ prime you would write $p_n+n=q\in\mathbb{P}$, where $\mathbb{P}$ denotes the set of all primes.

Answer 2

I think $p_n$ for the $n^\text{th}$ prime is quite common.

But what's great is that you can say "let $\ddot\smile{}_q$ denote the $q^\text{th}$ prime", and that's acceptable. You may call your variables whatever you want them to be called, as long as your statements are consistent.

Answer 3

In Maple, a computer algebra system, the ithprime(x) function is used. Also, I have seen $\pi(n)$, where $\pi(n)$ is the prime counting function, in books.

Regards, Matt