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 311
- 311 is the is the sum of the first three three-digit primes
- 311 is the smallest prime expressible as the sum of 3 consecutive palindromes
- 311 is the smallest prime that is the sum of two, three, and four consecutive composite numbers (311 = 155 + 156 = 102 + 104 + 105 = 76 + 77 + 78 + 80)
Common Properties of 311
The number n is deficient if the sum of all its positive divisors except itself is less than n.
Compare with perfect and abundant numbers.
The number n is evil if it has an even number of 1's in its binary expansion.
Guess what odious numbers are.
A number is odd if it is not divisible by 2.
Numbers that are not odd are even. Compare with another pair -- evil and odious numbers.
A prime is a positive integer greater than 1 that is divisible by no positive integers other than 1 and itself.
Prime numbers are opposite to composite numbers.
A number is said to be square-free if its prime decomposition contains no repeated factors.
A prime number is called a twin prime if there exists another prime number differing from it by 2.