Number Gossip

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Unique Properties of 7

  • 7 is the smallest number that cannot be represented as a sum of 3 squares
  • 7 is the smallest integer that is not the difference of two primes
  • There are 7 frieze groups, infinite discrete symmetry groups for patterns on a strip (infinitely wide rectangle)
  • The numbers on opposite sides of a regular die always add up to 7
  • 7 is the minimum number of colors that is always sufficient to color any map on a torus
  • 7 is the only prime followed by a cube
  • 7 is the smallest n for which a regular polygon with n sides cannot be constructed with ruler and compass
  • The Fano plane is the projective plane with the least number of points and lines: 7 each (submitted by Qiaochu Yuan)

Rare Properties of 7

Mersenne
Mersenne prime
Narcissistic
Palindromic prime

Common Properties of 7

Deficient
Happy
Lazy caterer
Lucky
Odd
Odious
Palindrome
Prime
Square-free
Twin