# 439 and Level 6

439 is a prime number, and it is also the sum of consecutive prime numbers in TWO different ways. Can you find either or both of those ways? You can write your answer or give or ask for hints in the comments.

In case someone is not sure what consecutive prime numbers are, here is an example: 17, 19, 23, 29, 31, and 37 are six consecutive prime numbers because they are ALL the prime numbers from 17 to 37 and they are listed in order. If we took their sum, we would get 156.

Print the puzzles or type the factors on this excel file: 12 Factors 2015-03-23

• 439 is a prime number.
• Prime factorization: 439 is prime.
• The exponent of prime number 439 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 439 has exactly 2 factors.
• Factors of 439: 1, 439
• Factor pairs: 439 = 1 x 439
• 439 has no square factors that allow its square root to be simplified. √439 ≈ 20.9523

How do we know that 439 is a prime number? If 439 were not a prime number, then it would be divisible by at least one prime number less than or equal to √439 ≈ 20.9523. Since 439 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, or 19, we know that 439 is a prime number.