NUMBER LOGIC / JD · 2026.10.19
Prime or Composite? How to Check a Number
Use square-root bounds and small divisibility tests instead of guessing.
The exact definitions
A prime number is an integer greater than 1 with exactly two positive divisors: 1 and itself. A composite integer greater than 1 has more than two positive divisors. The number 1 is neither prime nor composite.
A reliable test
To check whether 91 is prime, test possible prime divisors no larger than the square root of 91, which is a little under 10. Since 91 = 7 × 13, it is composite. No need to try every integer all the way to 90.
Common shortcuts and their limits
Even integers larger than 2 are composite. Integers ending in 5 are divisible by 5, but the number 5 itself is prime. Failing these quick filters does not prove primality; use the square-root test.
Practice with nearby numbers
Compare 97, 99, 101, and 121 using factors, not visual patterns. The dictionary entry for each in-range number provides another place to verify the result.