# Prime number theorem

## Statement

### Statement in terms of the asymptotic distribution in ratio terms

This states that:



where  is the prime-counting function: the number of primes less than or equal to , and  is the natural logarithm, i.e., the logarithm to base .

### Statement in terms of the logarithmic integral

This is a stronger formulation, which states that:

.

Here,  denotes the logarithmic integral.