The Magic of Prime Numbers & Internet Cryptography

In mathematics, prime numbers are the irreducible "atoms" of all positive integers. A prime number is a natural number strictly greater than 1 that cannot be formed by multiplying two smaller natural numbers.

1. The Fundamental Theorem of Arithmetic

Every integer greater than 1 is either a prime number itself or can be represented uniquely as a product of prime numbers (disregarding the order of factors).

2. Why Primes Protect the Internet (RSA Cryptography)

Every time you purchase an item online, check your bank account, or send an encrypted message, your browser relies on prime numbers. Multiplying two massive prime numbers (each hundreds of digits long) is lightning fast for computers:

However, doing the reverse—taking the resulting massive number N and finding its original prime factors p and q—is computationally impossible in reasonable time with known classical algorithms. This mathematical asymmetry is the bedrock of modern public-key cryptography.

3. The Sieve of Eratosthenes

Devised by ancient Greek mathematician Eratosthenes of Cyrene over 2,200 years ago, the Sieve is an elegant algorithm to find all prime numbers up to any specified limit by iteratively marking multiples of each prime starting from 2.