Number Gossip

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Unique Properties of 53

  • 53 is the smallest two-digit prime that does not produce a prime by adding a digit to it
  • 53 is the smallest multidigit balanced prime: primes which are the averages of their prime neighbors
  • 53 is the smallest prime number separated from the preceding and the following prime number by five non-prime numbers (that is 53 is the smallest number in the middle of two sexy prime pairs)
  • The month and day are simultaneously prime a total of 53 times in a leap year
  • 53 is the smallest prime p such that 1p1, 3p3, 7p7 and 9p9 are all prime
  • 100053 - 53 is prime: note that 53 is the smallest number with this property
  • 53 is the only two-digit number that equals its reverse in hexadecimal
  • 2 to the power 53 starts with 9: the first time 9 appears as the leading digit of a power of 2. The interesting part is that 9 is the last digit to appear as the leading digit of a power of 2

Common Properties of 53

Deficient
Evil
Odd
Prime
Square-free
Ulam