WHY?
deterministic 64-bitProof & factorization
Prime factorization97
CHECK · FACTOR · UNDERSTAND
Prime Number Checker
Find out whether a whole number is prime, see exactly why, then explore its factors and nearby primes.
64-bitdeterministic
localBigInt math
learnproof + practice
PRIMALITY CHECK
Enter a whole number
PRIME97 is prime
No divisor other than 1 and 97 exists.
Previous prime89
Next prime101
Prime gap12
Divisors2
DIVISIBILITY
before heavy mathFast checks
A composite number must have at least one factor at or below √n. For large 64-bit values, this page uses the deterministic seven-base Miller–Rabin test instead of pretending to trial-divide billions of candidates.
PRIME EXPLORER
segmented sieve · up to 5,001 valuesList primes in a range
25 primes25.0% of the range8 twin-prime pairs
DAILY 10
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Prime, composite, factors and next-prime questions rotate every day.
REFERENCE
Prime patterns worth knowing
1 is not prime
A prime has exactly two positive divisors. One has only one.
2 is special
Two is the only even prime. Every larger even integer is composite.
√n is enough
If n = a × b, one factor must be at or below √n. That is why a small divisor proves compositeness quickly.
Primes build integers
Every integer greater than one has a unique prime factorization, apart from order.
How the exact test workssmall factors · deterministic Miller–Rabin · factor witness
Inputs are parsed as JavaScript BigInt, never as floating-point Number. Small prime divisors are checked first. Remaining unsigned 64-bit values use a fixed seven-base Miller–Rabin set known to be deterministic across the entire 64-bit range.
Composite values are factored locally with small-prime division plus Pollard’s rho, so the result can show a concrete factor witness rather than only saying “not prime.” Range exploration uses a segmented sieve and is intentionally capped to keep the interface instant.