Number Gossip

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Unique Properties of 31

  • 31 is the earliest and the only known case such that the sum of the divisors of two distinct numbers (16 & 25) is the same prime quantity (31), that is to say: 1+2+4+8+16 = 31 and 1+5+25 = 31
  • 31 is the number of minimal composites which cover the set of composites in base 10
  • There are only 31 numbers which cannot be expressed as the sum of distinct squares
  • 31 = 22 + 33, i.e., the sum of the first two primes raised to themselves

Rare Properties of 31

Mersenne
Mersenne prime

Common Properties of 31

Deficient
Happy
Lucky
Odd
Odious
Prime
Square-free
Twin