The sieve of Eratosthenes (276 BC - 194 BC) is an ancient method for finding all prime numbers up to a specific given value. The concept is to progress through a chart of consecutive integers removing the multiples of each prime number, starting with the first prime number 2.

How it Works:
Start with a chart of consecutive positive integers. Multiples of the prime numbers will be crossed out throughout the chart. This chart will be from 1 to 100.

 1 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

 1 Cross out 1 (it is not a prime). 2 Start with 2. Circle 2 as a prime number, but cross out all multiples of 2 (every even number). 3 Now, move to the next prime 3. Circle 3 as a prime number, but cross out any multiple of 3 remaining in the chart. 4 Now, move to 5. Circle 5 as a prime number, but cross out any multiple of 5 remaining in the chart. 5 Now, move to 7. Circle 7 as a prime number, but cross out any multiple of 7 remaining in the chart. 6 Continue this process for each prime number you encounter on the chart. Remember that a prime is divisible only by 1 and itself. 7 The circled values in the chart are the prime numbers between 1 and 100.

The multiples of the values circled in black had already been colored,
or do not exist in this small chart.
The prime numbers between 1 and 100 are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97