Check if a number is prime, explore its properties, see factorization steps, find neighboring primes, and detect twin-prime pairs.
Supports large integers. Factorization of very large composites may take time.
Showing prime factorization for the number entered above.
Shows the nearest primes and prime gaps for the number entered above.
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Supports large integers beyond JavaScript's safe limit. Factorization of very large composites may require additional computation time.
A prime number is a positive integer greater than 1 that has exactly two positive divisors: 1 and itself. For example, 2, 3, 5, 7, 11, and 97 are prime numbers.
No. 1 is neither prime nor composite because it has only one positive divisor. Prime numbers must have exactly two distinct positive divisors.
No. 0 is neither prime nor composite. By definition, prime numbers are positive integers greater than 1.
No. The definition of prime numbers applies only to positive integers greater than 1. Negative numbers, zero, and one are not classified as prime.
The calculator tests whether any integer from 2 through the square root of the number divides it evenly. If none do, the number is prime. For very large numbers, it uses additional optimized algorithms.
Prime factorization breaks a composite number down into a product of prime numbers. For example, 360 = 2³ × 3² × 5. The calculator shows both the factor list and step-by-step division.
Twin primes are pairs of primes that differ by 2, such as (3, 5), (5, 7), (11, 13), or (29, 31). The calculator checks if your number is part of a twin-prime pair.
A prime gap is the difference between two consecutive prime numbers. For example, the gap between 89 and 97 is 8. The calculator shows gaps to the previous and next prime.
The calculator supports large integers beyond JavaScript's safe integer limit using BigInt arithmetic. Factorization of very large composite numbers may become computationally intensive — the calculator warns you when this happens.
The nth prime is the prime number that occupies position n in the sequence of primes. For example, the 25th prime is 97, and the 100th prime is 541.