Prime check, with factorisation for composites
Enter a whole number up to 10¹² and find out instantly whether it's prime — if it isn't, you also get its smallest factor, full prime factorisation and divisor count, plus the nearest prime before and after it.
How to use
- Enter a whole number (up to 1,000,000,000,000)
- Press Check
- Read the verdict, and for composite numbers, the factorisation and divisor count
Common questions
How large a number can this check?
Up to 1,000,000,000,000 (10¹²). It uses trial division skipping multiples of 2 and 3 (testing only 6k±1 candidates up to the square root), which keeps even a 10¹² check to at most about a million steps.
Why are 0 and 1 not considered prime?
0 has infinitely many divisors (every number divides it), and 1 has only one divisor (itself) rather than the two a prime needs. Both are explained on their own in the working panel rather than lumped in with ordinary composite numbers.
What's shown for a composite number?
Its smallest factor, its full prime factorisation, and its total divisor count (derived from the factorisation), alongside the nearest prime before and after it.