Prime Number Generator

Lists the first N prime numbers in order, starting from 2, where N is a count you choose between 1 and 500.

Enter how many primes you want; the list appears automatically, ready to copy with one click.

Requesting the first 10 primes returns `2, 3, 5, 7, 11, 13, 17, 19, 23, 29` — every one of these numbers has exactly two divisors (1 and itself), which is the definition of a prime.

Each candidate number is tested for divisibility by smaller numbers up to its square root — if nothing divides it evenly, it's prime — which is far more efficient than checking every number up to the candidate itself and still gives a mathematically exact answer, not an approximation.

Every even number greater than 2 is divisible by 2, so it automatically has at least three divisors (1, 2, and itself) and can't be prime; 2 itself is the sole exception, making it both the smallest prime and the only even one.

Prime numbers come up in cryptography (RSA key generation relies on large primes), hashing and hash-table sizing, number theory coursework, and puzzles or programming exercises that ask for prime-checking or prime-generation logic.

This generates up to 500 primes per request as an ordered list starting from 2 — it does not check whether an arbitrary large number you already have is prime, and it is not optimized for generating cryptographically large primes (hundreds of digits), which require specialized algorithms.

Calculation happens entirely in your browser; nothing is uploaded to a server.