## A Multiplication Based Logic Puzzle

### 499 and Level 5

499 is the sum of a nice bunch of consecutive prime numbers:

• 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 = 499. That’s 17 consecutive primes.

Print the puzzles or type the solution on this excel file: 12 Factors 2015-05-18

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• 499 is a prime number.
• Prime factorization: 499 is prime and cannot be factored.
• The exponent of prime number 499 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 499 has exactly 2 factors.
• Factors of 499: 1, 499
• Factor pairs: 499 = 1 x 499
• 499 has no square factors that allow its square root to be simplified. √499 ≈ 22.3383079

How do we know that 499 is a prime number? If 499 were not a prime number, then it would be divisible by at least one prime number less than or equal to √499 ≈ 22.3383. Since 499 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, or 19, we know that 499 is a prime number.

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