What is the 1st prime number?

By convention the sequence starts at 1: the 1st prime is 2, the 2nd is 3, the 3rd is 5, the 4th is 7, and so on.

How large an N can this tool handle?

The in-browser calculator comfortably handles N up to about 10,000 (the 10,000th prime is 104,729). For very large N the computation may take a second or two.

What algorithm is used?

Trial division testing odd integers up to the square root of the candidate. This is fast and memory-efficient for positions up to 10,000.

Is 1 considered a prime number?

No. By modern mathematical definition, 1 is not prime. The prime sequence begins at 2.

What is the 1000th prime?

The 1000th prime number is 7,919.

Nth Prime Calculator

Enter a position N and instantly find the exact prime number at that index (1-based).

Find the Nth Prime

Position N (single lookup)

Supports N from 1 to 10,000.

Range (list consecutive primes)

Range span capped at 200 primes.

Enter a position above to see results.

Quick Reference — Notable Primes

Position (N)	Prime	Note

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Summary

The Nth Prime Calculator finds the prime number that sits at a given position in the ordered sequence of primes. The 1st prime is 2, the 2nd is 3, the 3rd is 5, and so on. This tool computes the answer entirely in your browser using optimized trial division, with no server calls.

How it works

Enter a positive integer N in the input field.
The calculator iterates through natural numbers, testing each for primality.
It counts qualifying primes until it reaches the Nth one.
The result is displayed instantly along with a short prime sequence preview.
You can also enter a range (start N to end N) to list several primes at once.

Use cases

Verify prime-number homework or exam answers.
Generate test data for cryptography and algorithm exercises.
Explore the distribution of prime numbers at large positions.
Quickly look up well-known primes (100th, 1000th, 10000th).
Teach number theory concepts in a classroom or workshop.
Cross-check results from custom prime-finding code.
Support competitive programming practice (ICPC, Codeforces, etc.).

Frequently Asked Questions

Last updated: 2026-05-29 · Reviewed by Nham Vu