What are prime numbers?
Every whole number can be put into one of two categories:

Prime or Composite

Prime numbers are whole numbers that have exactly two factors: the number itself and 1.

(The number 1 is neither a prime number nor a composite number.)

Composite numbers - A number greater than 1 that is not a prime number is a composite number. A composite number has more than two factors and can be broken down by a method called prime factorization.

What is prime factorization?
All prime factorization is, is taking a composite number and splitting it up into the numbers that it's made up of until it can't be split any more.
This is a hundred chart, the circled numbers are prime numbers and the rest are composite numbers.

## Sieve of Erastosthenes

Eratosthenes is a famous mathematician of the third century BC who studied prime numbers. He designed a chart to identify prime numbers between two and a hundred (remember, one is neither prime nor composite). Here is a colored version of the sieve with directions below.

 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

 The Sieve of Eratosthenes can be constructed by writing the whole numbers from 2 to 100 in a rectangular array. The most common representation is ten by ten. We start with the first prime number, two- and color all multiples of two red. three- coloring its multiples green. five- multiples of five purple seven- multiples of seven orange. The numbers left in black are all prime numbers.

What are Twin Primes?

Twin primes are pairs of primes which differ by two.

The first twin primes are {3,5}, {5,7}, {11,13,} and {17,19}.