One academic outcome from this work was a challenge to Dunbar's number theorem.

This result has been superseded by the prime number theorem.

This is a considerable strengthening of the prime number theorem.

Euler's work in this area led to the development of the prime number theorem.

When am I going to have another smack at the prime number theorem?

They are used in the statement and proof of the prime number theorem.

He provided an unusually elementary proof of the prime number theorem.

The prime number theorem is a key result in this subject.

Another major milestone in the subject is the prime number theorem.

This statement is, in fact, equivalent to the prime number theorem.