431 and Level 5

431 is the sum of seven consecutive prime numbers beginning with prime number 47. What other prime numbers are in that sum? If you would like, you can type your answer in the comments.

2^431 (mod 431) = 2 so 431 is VERY likely a prime number. Scroll down past the puzzle to know for sure.

431 Puzzle

Print the puzzles or type the factors on this excel file:10 Factors 2015-03-16

  • 431 is a prime number.
  • Prime factorization: 431 is prime.
  • The exponent of prime number 431 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 431 has exactly 2 factors.
  • Factors of 431: 1, 431
  • Factor pairs: 431 = 1 x 431
  • 431 has no square factors that allow its square root to be simplified. √431 ≈ 20.7605

How do we know that 431 is a prime number? If 431 were not a prime number, then it would be divisible by at least one prime number less than or equal to √431 ≈ 20.7605. Since 431 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, or 19, we know that 431 is a prime number.

431 Logic

4 thoughts on “431 and Level 5

  1. A nice time-waster would have been to say “431 is the sum of seven consecutive prime numbers”. Better still: “431 is the sum of several consecutive prime numbers”. I imagine the first version wouldn’t take very long, but I’m not sure how I’d go about tackling the second version in a reasonably efficient way.

    • The way I worded it may seem like too easy of a question for you or me, but many others will still find it quite challenging. I think next time I will simply say, “431 is the sum of seven consecutive prime numbers, and one of them is 47. What are the others?”

  2. This is no doubt one of those facts that boggles my mind. I would have never thought that the sum of 7 consecutive primes would add up to a prime. This is a fine way to end the seventh day of the eleventh full week of the year.

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