## Thursday, February 24, 2011

### Manipulating digits from 1 to 9 to find prime numbers

Use the basic arithmetic operations and include the more advanced operations to find prime numbers

For example,

9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 45 = 3^2 * 5

9! + 8! + 7! + 6! + 5! + 4! + 3! + 2! + 1! = 409113 = 3^2 * 131 * 347
9! + 8! + 7! + 6! + 5! + 4! + 3! + 2! - 1! = 409111 = 569 * 719
9! + 8! + 7! + 6! + 5! + 4! + 3! - 2! + 1! = 409109 = 37 * 11057
9! + 8! + 7! + 6! + 5! + 4! + 3! - 2! - 1! = 409107 = 3 * 31 * 53 * 83
9! + 8! + 7! + 6! + 5! + 4! - 3! + 2! + 1! = 409101 = 3 * 7 * 7 * 11 * 11 * 23
9! + 8! + 7! + 6! + 5! + 4! - 3! - 2! + 1! = 409097 = 13 * 31469
9! + 8! + 7! + 6! + 5! + 4! - 3! - 2! - 1! = 409095 = 3 * 3 * 5 * 9091

9^8 + 7^6 + 5^4 + 3^2 + 1 = 43165005 = 3 * 5 * 13 * 41 * 5399

(No prime number so far)

9 - 8 + 7 - 6 + 5 - 4 + 3 - 2 + 1 = 5 is a prime number.

9 + 8^7 + 6^5 + 4^3 + 2^1 = 2105003 is a prime number

10! - 9! + 8! - 7! + 6! - 5! + 4! - 3! + 2! - 1! = 3301819 is a prime number
9! + 8! + 7! + 6! + 5! + 4! - 3! + 2! - 1! = 409099 is a prime number

Investigate with other combinations