Number Gossip

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Unique Properties of 1013

  • 1013 is the smallest prime with at least four digits in which every substring of length 3 is also prime
  • 1013 is the smallest prime such that after subtracting a thousand it remains a prime
  • 1013 is the smallest four-digit prime such that, if the digits are ABCD, then AB+CD and A+B+C+D are also primes
  • 1013 is the smallest four-digit prime such that simultaneously swapping the first two digits and the last two digits produces another prime

Common Properties of 1013

Deficient
Evil
Odd
Prime
Square-free