Patterns in Prime Numbers

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Mathematicians try to understand the patterns in the world. When they look at the natural numbers (1, 2, 3 . . .) they notice that one way the numbers can be organized was into two types of numbers: prime numbers and composite numbers. A prime number has exactly 2 factors 1 and itself, for example 11, is a prime number because the only numbers that divide equally into it are 1 and 11. Composite numbers have more than 2 factors, for example 4, is a composite number because 1, 2, and 4 can divide into it without having a remainder. One is not considered to be prime or composite since it has exactly 1 factor.
Different types of primes and some of what has been learned about prime numbers:
1. Around 300 BCE, Euclid proved that there are infinitely many prime numbers and that every natural number greater than 1 is either prime or can be written as a product of primes.