Number Theory: The Secret Life of Integers

Number theory is the math of which numbers behave nicely - and it is the reason your credit card number can travel over the internet without being stolen. This guide starts from prime fingerprints and builds up to the clock math that secures your browser.

1. Primes and the Building Blocks of Numbers A prime number is a number that cannot be built from smaller numbers. Every other number can be factored into primes in exactly one way, like a unique fingerprint. This phase shows why that matters and how to find the factors of any number.
2. The Clock Math You Already Know Modular arithmetic is the math of remainders and wrap-around. You already use it to read a clock. This phase extends that instinct into modular exponentiation, the Euclidean algorithm in disguise, and the reason the same math that tells you what time it is also secures your data.
3. How the Internet Stays Secret RSA encryption works because multiplying two large primes is easy, but factoring their product back apart is nearly impossible. This phase explains the one-way street that keeps your credit card number private, and connects it to the hashing and checksums you use every day.