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Instantly verify if any number is prime or composite. For composite numbers, our high-speed algorithm immediately computes the complete prime factorization. This free online tool allows you to check prime numbers quickly and accurately. No sign-up or installation required.
In number theory, a prime number is defined as a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. In other words, a prime number is only divisible by exactly two distinct positive divisors: 1 and itself.
Numbers that have more than two divisors are called composite numbers. The Fundamental Theorem of Arithmetic states that every integer greater than 1 either is a prime number itself or can be represented as the product of prime numbers. This means that primes are essentially the "atoms" from which all other numbers in mathematics are constructed.
For centuries, the study of prime numbers was considered "pure mathematics"—fascinating abstract concepts with absolutely no real-world application. That all changed drastically in the 1970s with the invention of modern computer science and cryptography.
Virtually all internet security, banking encryption, and secure messaging apps rely on the RSA algorithm. RSA works by multiplying two incredibly massive prime numbers together to create a public key. While multiplying them is easy, a computer trying to reverse-engineer (factorize) that massive number back into the two original primes would take millions of years.
In computer science, hash tables are data structures used to store information rapidly. Engineers use prime numbers to dictate the size of these tables because doing so dramatically reduces the rate of "collisions" (when two pieces of data try to occupy the exact same memory address), ensuring software runs lightning fast.
Around 300 BC, the ancient Greek mathematician Euclid published an elegant proof demonstrating that there is an infinite number of primes. No matter how high you count, you will always eventually find another prime number. However, as numbers get larger, prime numbers become increasingly rare and difficult to locate.
Today, global networks of supercomputers (like the GIMPS project) run 24/7 searching for the next largest known prime number, often containing tens of millions of digits!
Expert answers to common mathematical curiosities surrounding prime numbers.