May 7, 2025

Bethany Nguyen 

11th Grade

Fountain Valley High School

1, 3, 5, 29, 797. These are not just random numbers–they are the nearly indestructible bodyguards of your private data, bank account, and top-secret information. They are the backbone of security in the digital world, being divisible only by themselves and 1. In this day and age, everything is online, making these seemingly simple numbers now more essential than ever. 

The importance of prime numbers extends far beyond mathematics. In 1977, public-key cryptography made its dramatic debut, and it changed the digital age as we know it. Ron Rivest, Adi Shamir, and Leonard Adleman are the masterminds behind the RSA algorithm, revolutionizing the way encryption was performed by using two keys: one public and one private. The public key could be freely shared to hide encrypted messages, while the private key, possessed solely by the owner, served as the password used to decrypt them. 

Now, where do prime numbers come into play? The key to their power lies in the near impossibility of reversal. It’s a fairly simple process to multiply two prime numbers together. Try 61 × 53, for example. However, figuring out what two prime numbers multiplied to create 3,233 is a much harder process. It is an even harder process when the primes multiplied are hundreds, even thousands, of digits long. This task is one that would take powerful computers centuries to solve, making decryption practically impossible and not worth the result. 

In RSA, two large prime numbers are multiplied to create a public key. The original primes form the private key, known only to select individuals who can decrypt the information. This method of encryption is found everywhere. Secure data transmission in websites using HTTPS, digital signatures, and cryptocurrencies like Bitcoin is all made possible through this form of cryptography. Even secure government and military communications often use this encryption system to prevent interception of messages and information. From cloud storage to online voting to private browsing, prime numbers are crucial to the safety of our online world. 

The application of primes does not stop there. Algorithms such as the Diffie-Hellman key exchange allow two parties to create a shared secret key over an insecure network channel without ever directly exchanging the key, relying on modular arithmetic operations. Elliptic Curve Cryptography (ECC) is another modern method of encryption powered by primes that is both secure and efficient. Primes are the foundation of digital protection, employed by countless protocols and systems, creating a safe environment for private online activity.

While this complex practice is meant to be unbreakable, new developments come dangerously close to breaking it. Originating in 1994, Shor’s algorithm has proven that quantum computers, using quantum mechanical phenomena, have the power to factor large prime numbers far faster than typical computers. If this discovery advances far enough, RSA encryption could potentially become obsolete, leaving digital communications vulnerable to exposure. This threat drives researchers to begin exploring cryptography that can withstand threats from both classical and quantum computers. The future holds the possibility of entirely new mathematical methods of protecting data, resistant to attacks from a quantum-powered age. 

To most, primes are just numbers–but in the digital world, they are the invisible shield that keeps modern life secure. Cutting-edge cybersecurity has led prime numbers to become one of math’s most practical applications, safeguarding everything from banking to national secrets. And as threats evolve, scientific and mathematical research continues to shape life online. If there is one lesson to learn, it is that strength amidst uncertainty is often found in the simplest building blocks–thus, the power of prime.