Prime-counting function

Definition

For a real number $x$ , the prime-counting function $\pi(x)$ is the number of prime numbers $p$ with $p \le x$ .

Remarks

For example, $\pi(10) = 4$ , because the primes up to $10$ are $2, 3, 5, 7$ . Also $\pi(100) = 25$ . The function is a step function. It increases by $1$ at each prime. The prime number theorem says that $\pi(x)$ grows like $x / \ln x$ . The symbol $\pi$ here has no relation to the number $3.14159\dots$ .

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Divisibility definition
Prime number definition
Prime-counting function definition

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7 pages build on this one.

Tag	`0XRJB5SSNE`
URI	`m2://0XRJB5SSNE`
Kind	definition
Writing	W1 stated
MSC	11N05
Defines	Prime-counting function
Uses	Prime number

Prime-counting function

Definition

Remarks

Reading path

Where this leads

Further reading

What this page needs for W2

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