Number Theory & Cryptography
📋 What it is
A PRIME has exactly two factors (1 and itself); modular ("clock") arithmetic wraps numbers around.
🗣️ Coach says
Number theory studies whole numbers, and it secretly guards the internet. Primes are the atoms of numbers — 2, 3, 5, 7, 11… — and modern encryption relies on multiplying huge primes being easy while un-multiplying them is nearly impossible. MODULAR arithmetic wraps around like a clock: 10 + 5 hours = 3 o’clock (mod 12).
🧠 Memory hook
Primes = exactly two factors. Modular = wrap-around like a clock. Big primes lock your messages.
😂 Giggle
Why was the graph always making friends?
Because it was all about connections!
😲 Whoa!
The largest known prime has over 41 million digits — printed out, it would fill thousands of books.
✅ Quick check: Is 9 a prime number?
Say your answer out loud first — then reveal.
No — 9 = 3 × 3, so it has the factors 1, 3, and 9 (more than two).
A prime has EXACTLY two factors; 9 has three, so it is composite.
🪄 Trick question: Is 1 a prime number?
Careful — think it through, then reveal.
No — 1 has only ONE factor (itself), and a prime needs exactly two.
By definition a prime has two distinct factors; 1 falls short.
🧪 Try it! (2 minutes)
On a 12-hour clock, work out (9 + 7) mod 12. Then check by moving 7 hours past 9 o’clock.