prime number theorem

American  

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.

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Etymology

Origin of prime number theorem

First recorded in 1660–70

Example Sentences

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

From Slate • Jan. 22, 2016

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

From Slate • Jan. 22, 2016

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

From Slate • Jan. 22, 2016

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

From Slate • Jan. 22, 2016

Erdős later did a similar job of simplifying the prime number theorem, which reveals how prime numbers will be distributed.

From Scientific American • Mar. 26, 2013