Wheel Factorization - Example

Example

1. Find the first 2 prime numbers—2 and 3.

2. n = 2 · 3 = 6

3.

1 2 3 4 5 6

4. x = 1.
xn + 1 = 1 · 6 + 1 = 7.
(x + 1)n = (1 + 1) · 6 = 12.
Write 7 to 12 with 7 aligned with 1.

1 2 3 4 5 6 7 8 9 10 11 12

5. x = 2.
xn + 1 = 2 · 6 + 1 = 13.
(x + 1)n = (2 + 1) · 6 = 18.
Write 13 to 18.
Repeat for the next few lines.

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

6 and 7. Sieving

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

8. Sieving

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

9. Resultant list contains a non-prime 25. Use other methods of sieve to arrive at

2 3 5 7 11 13 17 19 23 29

Read more about this topic:  Wheel Factorization

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