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 whole number greater than 1 that has exactly two positive divisors: 1 and itself. This simple definition hides surprising depth — primes are considered the fundamental "building blocks" of all whole numbers, since every number greater than 1 can be expressed as a unique product of prime numbers, a fact known as the Fundamental Theorem of Arithmetic. This property makes primes central to number theory and, perhaps unexpectedly, to modern internet security.
Checking whether a number is prime becomes computationally more demanding as the number grows larger, since a naive check requires testing divisibility by every number up to its square root. For small numbers this is instant, but for the extremely large numbers used in real-world cryptography (hundreds of digits long), specialized primality testing algorithms are required, since brute-force checking would take longer than the age of the universe.
RSA encryption, one of the most widely used cryptographic systems protecting online communication, relies on the mathematical difficulty of factoring the product of two very large prime numbers back into its original primes. This asymmetry — multiplying two large primes together is fast, but factoring the result back into those primes is extraordinarily slow — is precisely what makes RSA encryption secure, turning a seemingly abstract mathematical property into the backbone of secure online banking, shopping, and communication.
Mathematicians and distributed computing projects continue searching for increasingly large prime numbers, with the largest known primes now having tens of millions of digits, found using specialized algorithms and massive computational resources distributed across volunteer computers worldwide. While these enormous primes have limited direct practical use, the search has driven genuine advances in computational number theory and testing algorithms.
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.
