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.