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 191
- 191 is the smallest palindromic prime whose sum of digits is a multidigit palindromic prime
- By adding up the values of the common US coins, one obtains 191 cents (silver dollar + half dollar + quarter + dime + nickel + penny)
- 191 is the smallest palindromic prime such that the next palindromic prime has the same non-zero digit's product (the next palindromic prime is 313)
- 191 is the larger of the first occurrence of two successive primes using no prime digits (181, 191)
- 191 is the smallest multidigit palindromic prime that yields a palindrome when multiplied by the following prime
- 191 is the largest three-digit mountain prime
Common Properties of 191
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 n-th lazy caterer number is the maximum number of pieces a (circular) pizza can be cut into with n (straight-line) cuts.
Unlike the situation with cake, everybody gets the toppings.
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.
The number n is odious if it has an odd number of 1's in its binary expansion.
Guess what evil numbers are.
A palindrome is a number that reads the same forward or backward.
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.
Undulating numbers are numbers of the form abababab... in base 10.
This property is significant starting from 3-digit numbers, so we will not consider numbers below 100.