Prime Density

[Thelonious]

I was having a great time watching The Prime Number Shitting Bear and I noticed it keeping track of "prime density." It seems there is a hole in my education. Could someone please explain what prime density is and how it is calculated?

[Qfwfq]

Prime density is usually defined, for a given number n, as the count of primes less than n, divided by n.

According to the prime number theorem, for increasing n it will be more and more like n divided by ln n.

[Thelonious]

I see.

Forgive me, but what is the significance of prime density? I cannot think of any application or advantage to knowing prime density.

[Qfwfq]

Originally Posted by Thelonious

I cannot think of any application or advantage to knowing prime density.

Neither can I see any application or advantage to that bear!

Primes have many uses, including cryptographic techniques, and it is handy to have an idea of how many primes there are up to some large number.