Prime number theorem
From Number
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.