Free Online Prime Number Checker

1. Type a positive integer in the input field (the tool uses BigInt for arbitrary size).
2. Read whether the number is prime or composite.
3. Check the previous and next primes printed alongside for context.

A prime has exactly two positive divisors: 1 and itself. The first few are 2, 3, 5, 7, 11, 13, 17, 19. By convention 1 is not prime (it has only one divisor) and 2 is the only even prime. Primes are the building blocks of integer arithmetic — every positive integer has a unique prime factorization, the Fundamental Theorem of Arithmetic.

This tool uses deterministic Miller-Rabin primality testing with a fixed witness set, which is provably correct for all 64-bit integers and stays sub-millisecond even for very large values. Trial division would slow to a crawl past a few million.

In addition to the yes/no answer the checker prints the next prime above the input and the previous prime below — useful when picking primes for cryptographic key generation, hash-table sizes, or recreational number theory.