Prime Factorization & Euclid's Algorithm
Building on the prior lesson of the Division Algorithm and Modular Arithmetic, we move onto Prime Factorization and Euclid’s Algorithm. These are not only extremely interesting facets of math and number theory, but one of the most utilized pieces of math in the modern digital world. Prime Factorization is fundamental to almost all encryption, and it is by the sheer scale of the math that allows it to be so — for even simple encryption breaking, a conventional computer could take over a hundred years running full bore before it could crack some types of encryption. This is also what makes things like Quantum Computers so terrifying — they have the capacity to break prime factorization, and thus, our entire modern digital security infrastructure. ...