Check if a number is prime, generate lists of prime numbers in any range, find the Nth prime, and perform prime factorization. Free, instant, and 100% client-side.
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. This calculator provides four powerful tools: a prime checker to test any number, a prime generator using the Sieve of Eratosthenes algorithm, an Nth prime finder, and a prime factorization tool that breaks down any composite number into its prime factors.
A prime number is a natural number greater than 1 that has exactly two factors: 1 and itself. For example, 2, 3, 5, 7, 11, and 97 are prime numbers. The number 1 is not considered prime.
The prime generator uses the Sieve of Eratosthenes algorithm, one of the most efficient methods for finding all primes up to a given limit. It works by iteratively marking the multiples of each prime starting from 2.
Prime factorization is the process of breaking down a composite number into a product of prime numbers. For example, 360 = 2³ × 3² × 5. Every composite number has a unique prime factorization (Fundamental Theorem of Arithmetic).
This calculator supports numbers up to 10,000,000 (10 million) for generation and checking. For factorization, it can handle numbers up to 1 trillion (10¹²) efficiently.