## A Multiplication Based Logic Puzzle

### 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 and cannot be factored.
• 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.

#### Comments on: "439 and Level 6" (6)

1. 139+149+151 was nice and easy; finding 31+37+41+43+47+53+59+61+67 took a bit more work!

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• ivasallay said:

You’ve certainly proven that you can find the consecutive primes! I’ll present more of these challenges in the future.

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2. Every time I read the rule about how to test if it’s a prime number I get a little closer to remembering it. But even if I ever do remember it I will still like reading the rule, 439 just has that prime look to it…

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• ivasallay said:

We can often tell a number is composite by just looking at it, but every prime number still has to be proven that it’s prime. You’ll eventually remember the rule, I’m sure. Thanks for reading faithfully!

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3. I couldn’t resist a quick tessellation of your recent prime, 439, which is of the form 3n+1, so might be a Trefoil Lattice Labyrinth and indeed is, as 439 is a Loeschian Number of form a^2 +ab+b^2, being 18^2 + 18×5 + 5^2. I’ll shortly add Trefoil (18,5) on to the Wedding Anniversary post on latticelabyrinths.net as I don’t think that by itself it merits a new post. Each trigonally symmetrical supertile consists of 439 triangles.

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• ivasallay said:

I can’t wait to see it!

I think it would be fine to have any of your creations be a post all by themselves. It is generally easier for me to read several short post rather than one long one, and I imagine many people feel the same way. Besides several people who have seen the original post might not know to look at it again to see more tessellations.

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