Notes on Primes

Good Morning, and happy Friday!
My weekly blog post this week will steer back towards mathematics!
I recently made some quick notes on prime numbers and thought I would share them with you.
Enjoy!

Practical uses of prime numbers...

Well to begin with, there aren't that many. Prime numbers have many interesting uses in mathematical theory, but out in the real world, they are mainly used in programming, random number generators, and especially cryptography.

Programming uses prime numbers to check for mistakes in code, create random samples and random numbers.

Random number generators use prime numbers to search for and find random numbers to generate / compile data.

Cryptography goes back a long time. Spies would use all sorts of ways to encrypt data, from using dictionaries, to random books, to codes number sequences. Currently, RSA and other encryption systems use large primes and prime factorization (I'll get to this in a bit) to create really difficult codes to break. Since we do not even know all the prime numbers in the world, it is extremely hard to break RSA encryption.

Prime factorization is a principle key in mathematics. The fundamental theorem of algebra states:

Every integer greater than 1 is either a prime, or the product of prime numbers, and this product is unique, up to the order of the factors.

Euclid stated this theorem in his book Euclid's Elements. The idea that any positive integer is either prime or a product of primes is sort of baffling! In a sense, to think that every number is directly related to prime numbers seems to suggest a great significance to these numbers, but we haven't really done that much with them over the years.

Me personally, I think that God just loves numbers. :)

-SheepDog-