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]

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.