Number Gossip

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Unique Properties of 728

  • Consecutive Smith numbers are called Smith brothers: 728 is the smaller brother of the smallest pair of Smith brothers
  • 728 is the smallest number n where n and n+1 are both products of 5 or more primes
  • 728 is the smallest Fermat-near-miss number: it differs by 1 from a cube and it is a sum of two cubes
  • 728 is the smallest number that is the sum of two (possibly negative) cubes in at least 3 ways, in other words it is the third cabtaxi number
  • 728 is the smallest product of three positive integers (8,7,13) giving a solution to the Diophantine equation x3 − y3 = z3
  • 728 is the smallest number n with property that n and 2n are sums of two distinct positive cubes (728 = 63 + 83 and 1456 = 53 + 113)

Common Properties of 728

Smith (Joke)