Prime Numbers

RSA Algorithm Rivest-Shamir-Aldeman Algorithm an asymmetric cryptography algorithm utilizes public and private generated from large prime numbers used to encrypt and decrypt data. The public key consists of two numbers where one number is a multiplication of two prime numbers. The private key is also derived from the same two prime numbers meaning if the public key primes are compromised, then so is the private key. Φ Φ(Phi) counts the number of numbers that are less than or equal to n and only share the factor of 1 with n Geeks for Geeks example: Geek For Geeks: RSA Algorithm Cryptography...

Greatest Common Divisor GCD The largest number $n ∈ Z+$ that is a factor of both nonzero $x$ & $y$ such that both $n | x$ & $n | y$ are true. Relatively Prime Two numbers $x$ and $y$ are said to be relatively prime if and only if their GCD is 1. In other terms: $$∄ n ∈ Z+ > 1$$ where both $n | x$ and $n | y$ are true....

Prime & Composite Relationship: If $p ∈ Z+$ and $p > 1$, then $p$ is either prime or composite. Prime Numbers: If $p ∈ Z+$ and $p > 1$, then $p$ is prime if the the only factors of p are $1$ & $p$. Composite Numbers: If $p ∈ Z+$ and $p > 1$, then $p$ is composite if $p$ if $∃ a ∈ Z+$ such that $a | p$ & $1 < a < p$....