Unlocking Cryptography: The Vital Role of Prime Numbers 🔐

Prime numbers are commonly referred to as the “atoms” of the numerical realm, for they are the fundamental, indivisible units that make up every number. For instance, 10 can be written as a product of 2 and 5, two prime numbers. Or, 150 as a product of 15 and 10, which can be further broken down and written as the product of 3, 5, 2 and 5 – all prime numbers. Or a larger number such as 126, 356, which is composed of larger prime numbers 2,2,31, and 1019.

This process of reducing a composite number to a product of prime numbers is known as prime factorization. For a computer, multiplying two prime numbers, each even 100 digits long, isn’t that difficult; however, factoring the product back into its components is notoriously difficult, even for supercomputers. For this very reason, prime numbers are used in cryptography.

It is difficult to find the prime factors of a composite number without knowing the factors to begin with. This makes it difficult for someone to intercept a message and read it without the proper key.

#primenumbers #factorization #cryptography

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References:
https://math.berkeley.edu/~kpmann/encryption.pdf
https://cryptofundamentals.com/primes

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