Number Gossip

(Enter a number and I'll tell you everything you wanted to know about it but were afraid to ask.)

Unique Properties of 3

  • 3 is the greatest number of consecutive integers that can be pairwise relatively prime
  • 3 is the only prime sandwiched between a prime and a composite number
  • 3 is the only prime followed by a square
  • Every positive integer is the sum of at most 3 triangular numbers
  • If the n-th Fibonacci number is prime, then n must itself be prime, with the exception of 3, which is the 4th Fibonacci number
  • 3 is the only number which is equal to the sum of all the natural numbers less than it
  • 3 is the only triangular number that is also prime

Rare Properties of 3

Fibonacci
Mersenne
Mersenne prime
Narcissistic
Palindromic prime

Common Properties of 3

Deficient
Evil
Lucky
Odd
Palindrome
Prime
Square-free
Triangular
Twin
Ulam