prime number theorem

noun

, Mathematics.

1. the theorem that the number of prime numbers less than or equal to a given number is approximately equal to the given number divided by its natural logarithm.

Word History and Origins

Origin of prime number theorem¹

First recorded in 1660–70

Example Sentences

The prime number theorem states that the average gap between prime numbers increases without bound as you go out on the number line, but recent work towards the twin prime conjecture shows that there are infinitely many pairs of primes that differ by only 246.

From Scientific American

We don’t know the exact answer, but the prime number theorem gets us close enough.

From Slate

Another visit to the prime number theorem shows there are approximately 1017,425,163 primes less than the next-largest known prime.

From Slate

The prime number theorem, first proved in the late 1800s, quantifies that decline.

From Slate

We can use the prime number theorem to estimate how many missing primes there are between M74207281 and the next smallest prime.

From Slate