## A Multiplication Based Logic Puzzle

### 419 and Level 1

2^419 (mod 419) = 2 so 419 is VERY LIKELY a prime number. Scroll down past the puzzle to know for sure.

Print the puzzles or type the factors on this excel file: 12 Factors 2015-03-09

• 419 is a prime number.
• Prime factorization: 419 is prime and cannot be factored.
• The exponent of prime number 419 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 419 has exactly 2 factors.
• Factors of 419: 1, 419
• Factor pairs: 419 = 1 x 419
• 419 has no square factors that allow its square root to be simplified. √419 ≈ 20.4695

How do we know that 419 is a prime number? If 419 were not a prime number, then it would be divisible by at least one prime number less than or equal to √419 ≈ 20.4695. Since 419 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, or 19, we know that 419 is a prime number.

#### Comments on: "419 and Level 1" (4)

1. No factors, not a sum of two squares not a Loeschian number (a^2 + ab +b^2) – flinty, indivisible, primly prime 419!

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• abyssbrain said:

Well. at least, (419×2^2n)/3 cannot be prime for any value of n. (I wont post the proof though since its too long 🙂 )

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• Crikey! hang on, though, your expression isn’t an integer.

Would you like to specify two colours that go together well for your tessellation, specified either as CMYK or RGB or just as “blobs” I can copy.

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• abyssbrain said:

I think that CMYK would be good.

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