What Makes a Number Prime
Primes are the atoms of arithmetic: every whole number greater than 1 is either prime or a unique product of primes (the Fundamental Theorem of Arithmetic). They secure your bank transactions, generate secure keys, and still hide unsolved mysteries — nobody knows if there are infinitely many twin primes.
The Trial Division Shortcut
To test n, you only need to trial-divide up to √n. Why? If n had a factor larger than √n, its partner factor would be smaller than √n — and you would already have found that one. For 97, that means testing just 2, 3, 5, and 7.
Special Cases to Memorize
- 1 is neither prime nor composite.
- 2 is the only even prime — every other even number is divisible by 2.
- 0 and negatives are not prime by definition.
Breaking numbers into prime factors? Try our factoring calculator.