Factor and Verify

Pick any number under 100 and factor it into primes. Try 84. Divide by the smallest prime: 84 ÷ 2 = 42, ÷ 2 = 21, ÷ 3 = 7. So 84 = 2² × 3 × 7. Check: 4 × 3 × 7 = 84.

Now the prime test. Is 97 prime? You only need to check divisors up to √97 ≈ 9.85. Test 2, 3, 5, 7. 97 isn't even. 9+7 = 16, not divisible by 3. It doesn't end in 0 or 5. None divide evenly. 97 is prime.

Try a larger one. 143? √143 ≈ 11.96. Test 2, 3, 5, 7, 11. 143 ÷ 11 = 13. So 143 = 11 × 13 — not prime.

Three factorizations in your head each morning, and prime-spotting becomes automatic — the skill cryptographers need and attackers hope you never learn.