Number Gossip

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Unique Properties of 91

  • 91 is the smallest positive integer expressible as a sum of two cubes in two different ways if negative cubes are allowed: 91 = 63 + (-5)^3 = 43 + 33
  • 91 is the first non-trivial composite: every smaller composite is either even, a familiar square, ends in 5, has a digit sum that is a multiple of 3, or is obviously divisible by 11
  • In cents of a U.S. dollar, 91 is the amount of money one has if one has one each of the coins of denominations less than a dollar (penny, nickel, dime, quarter and half dollar)
  • 91 is the smallest pseudoprime to base 3
  • 91 is the smallest Cuban composite, that is the smallest composite number equal to the difference of two consecutive cubes
  • 91 is the smallest number which is both the sum and the difference of two consecutive positive cubes (submitted by Anthony Kozar)

Common Properties of 91