Check if a number is prime and find all its prime factors instantly.
A prime number is a natural number greater than 1 that has exactly two divisors: 1 and itself. Examples include 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. Our prime number checker instantly tells you whether any number is prime and finds all prime numbers up to any limit using the Sieve of Eratosthenes algorithm.
To check if a number N is prime: test divisibility by all numbers from 2 to √N. If none divide evenly, N is prime. For example, to check if 37 is prime: √37 ≈ 6.08, so test 2, 3, 4, 5, 6. None divide 37 evenly, so 37 is prime. Our calculator performs this check instantly for numbers of any size.
The Sieve of Eratosthenes is an ancient algorithm for finding all primes up to a given limit. Start with a list of numbers 2 to N. Mark 2 as prime, then cross out all multiples of 2. Move to the next unmarked number (3), mark it prime, cross out its multiples. Continue until you reach √N. All remaining unmarked numbers are prime.
Prime numbers are the foundation of modern internet security. RSA encryption — used to secure your banking, email, and shopping — works because it is mathematically easy to multiply two large primes together but computationally impossible to factor the result back into its prime components. A 2048-bit RSA key uses primes with about 300 digits each.
2 is the only even prime number. Every other even number is divisible by 2, making them composite. There are infinitely many prime numbers — proven by Euclid around 300 BC. Twin primes (pairs like 11,13 and 17,19) are primes that differ by 2 — whether there are infinitely many is an unsolved mathematical problem. The largest known prime number has over 24 million digits.
A prime number is a natural number greater than 1 that has no divisors other than 1 and itself. Examples: 2, 3, 5, 7, 11, 13.
No. 1 is not considered a prime number by mathematical definition. Prime numbers must have exactly two factors: 1 and themselves.
The largest known prime numbers are Mersenne primes with millions of digits, discovered using distributed computing projects like GIMPS.
Prime numbers are fundamental to cryptography and internet security. RSA encryption, used to secure online transactions, relies on the difficulty of factoring large primes.
