Prime Number Generator

Generate prime numbers efficiently using the Sieve of Eratosthenes algorithm. Find all primes within a specified range or generate the first N prime numbers. Perfect for mathematical research, educational purposes, and programming challenges.

Find the Nth Prime Number

1st prime = 2, 2nd prime = 3, 3rd prime = 5, ...

Quick Reference

Prime #10

29

Prime #100

541

Prime #1,000

7,919

Prime #10,000

104,729

FAQ

How does the Sieve of Eratosthenes work?

Starting with all numbers marked as potential primes, iteratively mark multiples of each prime as composite. Numbers remaining unmarked are prime. This ancient algorithm is highly efficient for finding all primes up to a limit.

How many prime numbers are there?

There are infinitely many primes, proven by Euclid over 2000 years ago. However, they become increasingly sparse as numbers get larger. The Prime Number Theorem describes their distribution.

What is the largest known prime?

The largest known primes are Mersenne primes (2^p - 1). The Great Internet Mersenne Prime Search (GIMPS) continues to find new record primes, with the largest having tens of millions of digits.

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