How Do Prime Numbers Protect Our Data?

When you hear the term prime number, you probably think of math class. For many, it was just a dry definition to memorize in school, with little hint of what it’s actually used for.

However, prime numbers play a very important role in modern technology. Without them, the internet, online banking, and even messaging would be far less secure today.

Why are they special?

A fundamental rule of mathematics states that every integer greater than 1 can be factored into a unique combination of primes, meaning there is only one combination of primes for any given number.

For example:

• 12 = 2 × 2 × 3
• 30 = 2 × 3 × 5
• 84 = 2 × 2 × 3 × 7

But what does this have to do with the internet?

Much more than we might think.

When you log in to your online bank, shop online, or send an encrypted message, encryption algorithms work in the background using very large prime numbers to keep the connection secure. The most famous example of this is RSA encryption.

Imagine multiplying two very large prime numbers. A computer can do this extremely quickly, even if the numbers contain hundreds or even thousands of digits. However, the reverse task is much more difficult.

Working backward from the product to find the original primes is an enormously difficult computational task.

This is exactly what the security of RSA is based on.

Put simply, the idea is this: we encrypt the information using an algorithm that uses the product of two prime numbers, but to decrypt the encrypted information, the two prime numbers must be known. So, if we want to exchange encrypted messages with a website, we can use the product of two large prime numbers for encryption. The encrypted message can then only be decrypted by the website that knows the original two prime numbers.

How large are the prime numbers we are talking about?

Modern encryption does not use prime numbers consisting of only one or two digits. Prime numbers hundreds of digits long are common.

They are found and verified using special algorithms.

An interesting fact is that, at the time of writing this article in 2026, the largest known prime number was discovered in 2024 and consists of 41,024,320 million digits.

Where do you encounter them in everyday life?

Without realizing it, you use them almost every day.

For example, when you:

• use online banking
• pay by credit card
• open an HTTPS website
• send an email
• start a video call
• shop online

The encryption systems running in the background are often based on prime numbers.

Is all digital security built on prime numbers?

Not entirely. Security depends on many factors, including:

• the encryption algorithm being used
• the length of the key, meaning how large the prime numbers are
• software vulnerabilities
• and whether users manage their passwords properly

However, prime numbers are among the most important building blocks of modern public-key encryption.

What would happen if someone could factor numbers quickly?

If a method were discovered to factor enormous numbers into primes effortlessly, today’s digital security infrastructure would essentially collapse overnight.

This risk is why researchers around the world are developing new forms of encryption known as post-quantum cryptography. Since future quantum computers may solve certain mathematical problems much faster than today’s computers, new quantum-resistant encryption standards are already being introduced.

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