Nth prime number calculator
Enter a position n to get the prime in that place, where the 1st prime is 2 and the 2nd is 3. It uses a full sieve, not an estimate.
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Processing and privacy: The result is calculated inside your browser and your data is not sent to any server.
How to use it
- Enter position n.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Sieve up to the proven bound p(n) < n × (ln n + ln ln n) for n ≥ 6, then count primes until position n.
Example
Inputs: Position n = 100. Result: Prime number 100: 541; Previous prime: 523; Next prime: 547.
Limits and caveats
- n runs from 1 to one million.
- Counting starts with 2 as the 1st prime.
Questions about this tool
What is the 100th prime?
541, and the 1000th prime is 7919.
What is the millionth prime?
15485863.
Is there a direct formula for the nth prime?
No practical simple formula exists, so the tool sieves up to a proven bound and counts.