Primes of Life Eratosthenes of Cyrene lived approximately 275-195 BC. He was the first to estimate accurately the diameter of the earth. He was highly regarded in the ancient world, but unfortunately only fragments of his writing have survived. One of his living contributions is the "Sieve of Eratosthenes," a method for identifying prime numbers. A prime number is a natural number greater than 1 that can be divided without remainder only by itself and by 1. Natural numbers that can be divided by a number less than itself and greater than 1 are composite numbers. Try to identify all prime numbers up to 100 using the "Sieve of Eratosthenes." Choose five different color markers and print out the 100 chart. Shade in the number 1 square with the red marker. It is special and unique. Do you know why? Think about this: Is 1 prime? Think about what it means to be prime. We said it was a number that can only be divided by 1 and itself without a remainder. But 1 is itself. Are you confused yet? You should be. This is confusing stuff! It is like defining a word by using the word itself. For example: "blue" is the color that makes blue. Silly isn't it! But that's why we don't consider 1 prime. Now, is 1 a composite? Of course not. The only number that makes up 1 is 1. So, the number 1 is neither prime nor composite. And that's why it's a special number! The number 2 is the first prime number. Shade in all the multiples of 2 with the second marker. What pattern formed by shading all the multiples of two? Straight horizontal lines are formed. It eliminates all even numbers because they are all multiples of two. The number 3 is the first odd number. Shade in all the multiples of 3 with the third marker that have not been shaded with the second marker. How can you describe the pattern formed? Which numbers are multiple of two and three? Diagonals are formed! The multiples of two and three are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, and 96. The number 5 is the second odd number. Shade in all the multiples of 5 with the fourth marker that have not been shaded in with the second and third marker. How can you describe the pattern formed? Which numbers are multiples of two, three and five? One straight, horizontal line is formed. The multiples of two, three, and five are 30, 60, and 90. The number 7 is the third odd number. Shade in all the multiples of 7 with the last marker that have not been shaded in with the other markers. How can you describe the pattern formed by the last marker's squares? There is no pattern! There are no multiples of two, three, five, and seven. The least common multiple is 210. The numbers not shaded in are 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. These numbers are prime because they are greater than 1 and can be divided without remainder only by itself and by 1. Did you know there are 25 total prime numbers less than 100. Remember to include 2, 3, 5, and 7 when counting!