Enter any number to check if it is prime. Get the prime factorization, number of divisors, and nearby primes.
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The first primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. The number 2 is the only even prime. Every integer greater than 1 is either prime or can be uniquely expressed as a product of primes (the Fundamental Theorem of Arithmetic). Primes are the "building blocks" of all integers.
Enter any positive integer and the calculator instantly determines whether it is prime. If the number is not prime (composite), it shows the complete prime factorization. The calculator also finds the nearest primes above and below the entered number and lists all primes up to a specified limit.
Prime numbers are fundamental to modern cryptography. RSA encryption, which secures internet banking, email, and online transactions, relies on the difficulty of factoring the product of two very large primes. A 2048-bit RSA key involves primes with over 300 digits. While finding large primes is computationally feasible, factoring their product is astronomically difficult, which is what makes the encryption secure.
Prime numbers are the foundation of modern internet security. RSA encryption, which protects online banking, email, and e-commerce, relies on the mathematical difficulty of factoring the product of two very large prime numbers. Breaking RSA encryption would require factoring numbers with 600+ digits, a task that would take classical computers longer than the age of the universe. The largest known prime number (as of recent records) has millions of digits, discovered by the Great Internet Mersenne Prime Search (GIMPS) distributed computing project. In number theory, primes follow fascinating patterns: the twin prime conjecture suggests there are infinitely many pairs of primes that differ by 2 (like 11 and 13, or 29 and 31). The Riemann Hypothesis, one of the most important unsolved problems in mathematics, concerns the distribution of prime numbers.