15 May 2020

iad58: (Default)
  • 53 appears to be the smallest number of squares on a standard chessboard attacked by eight queens.
  • 100053 − 53 is prime. Note that 53 is the smallest number with this property.
  • The sum of the first 53 primes is 5830, which is divisible by 53, a property shared by few other numbers.
  • 53 in decimal is 35 in hexadecimal. Four additional multiples of 53 share this property: 371 = 173₁₆, 5141 = 1415₁₆, 99481 = 18499₁₆, and 8520280 = 082025816. Apart from the trivial case of single-digit decimals, no other number has this property.
  • The reversal of 53 (that is, 35) equals the sum of digits of 53³.
  • The month and day are simultaneously prime a total of 53 times in a leap year.
  • The chance that no pair of 53 people in a room have the same birthday is approximately 1/53.

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