Prime Counting Calculator
Count the primes up to N and compare with the N ÷ ln(N) estimate.
What is Prime Counting?
π(N) is the number of primes less than or equal to N: 25 below 100, 168 below 1,000, 78,498 below a million. Its growth is the subject of the prime number theorem — π(N) is roughly N ÷ ln(N), an estimate that keeps getting relatively better as N grows even though the primes themselves get rarer.
How it works
A single sieve pass counts and lists every prime up to N, so the count and the list can never disagree. The prime-number-theorem estimate and its percentage error are computed beside the true count, which turns a lookup into the comparison the theorem is actually about.
- Enter your input. Type or paste your input into the field above — the tool responds instantly.
- Review the result. Output updates live as you type. Everything runs entirely in your browser.
- Copy or download. Use the Copy button to grab the result, or Download to save it as a file.
Examples
Realistic sample
Type or paste any realistic input — the tool computes the result locally and instantly.
Common mistakes
Expecting a server round-trip
Nothing is uploaded — every tool in this category runs entirely in your browser.