Gambling with Secrets: Part 2/8 (Prime Factorization)

Euclid of Alexandria formalized around 300 BC the principle that all integers split into exactly two categories—prime numbers that cannot share equally and composite numbers that divide into equal parts.

Ancient humans developed counting methods to track the moon’s cycles, creating notches on artifacts or using numerals where each mark represented one unit like a single day between lunar phases.

Mathematicians factor composite numbers by finding all prime numbers that divide evenly into the target, repeatedly breaking it down until only indivisible prime components remain.

Ancient mathematicians discovered prime numbers when attempting to divide quantities like the 29-day lunar cycle into equal parts, finding certain numbers resist all efforts to split them into equal integer groups.

Mathematicians arrange integers in an outward-growing spiral starting from the center and coloring all prime numbers, revealing unexpected diagonal line patterns when viewing millions of numbers simultaneously.

Every integer possesses exactly one prime factorization, making this decomposition function like a unique key that unlocks only one specific number, with no two numbers sharing identical prime factor combinations.