508 A Mathematical and Biblical Truth: 2 > 1

Two Is Better Than One Because...

Two are better than one; because they have a good reward for their labour.

For if they fall, the one will lift up his fellow: but woe to him that is alone when he falleth; for he hath not another to help him up.

Ecclesiastes 4: 9 – 10

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508 is the sum of some consecutive prime numbers, and at least one of those prime numbers is in its prime factorization. Can you figure out what those consecutive primes are?

  • 508 is a composite number.
  • Prime factorization: 508 = 2 x 2 x 127, which can be written 508 = (2^2) x 127
  • The exponents in the prime factorization are 2 and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1) = 3 x 2  = 6. Therefore 508 has exactly 6 factors.
  • Factors of 508: 1, 2, 4, 127, 254, 508
  • Factor pairs: 508 = 1 x 508, 2 x 254, or 4 x 127
  • Taking the factor pair with the largest square number factor, we get √508 = (√4)(√127) = 2√127 ≈ 22.53 88 55 33 9

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