A factor tree is a way to visualize a number's prime factors.
Some numbers make geometric shapes when arranged as a collection of dots, for example, 16 makes a square, and 10 makes a triangle.
This important result says that every natural number greater than one can be expressed as a product of primes in exactly one way.
Modular arithmetic, also known as "clock math," incorporates "wrap around" effects by having some number other than zero play the role of zero in addition, subtraction, multiplication, and division.
A prime number has no factors other than 1 and itself. Primes are the fundamental building blocks of arithmetic. The fundamental theorem of arithmetic says that each whole number can be uniquely decomposed into products of primes.
We can think of the space between primes as "prime deserts," strings of consecutive numbers, none of which are prime.
Public key encryption allows two parties to communicate securely over an un-secured computer network using the properties of prime numbers and modular arithmetic. RSA is the modern standard for public key encryption.
This is the modern standard for data security on the internet. It uses properties of prime numbers and modular arithmetic.
The answer to the question of why the primes occur where they do on the number line has eluded mathematicians for centuries. Gauss's Prime Number Theorem is perhaps one of the most famous attempts to find the "pattern behind the primes."
This famous, as yet unproven, result relates to the distribution of prime numbers on the number line.