167 (number)

167 is the natural number following 166 and preceding 168.

It is a prime number, a safe prime and an Eisenstein prime with no imaginary part and a real part of the form $3n\; -\; 1$. Since the next odd number, 169, is a square of a prime, 167 is a Chen prime.

It is also the smallest number "k" with exactly 15 solutions to the equation "x" - φ("x") = "k", making it a highly cototient number.

It is the smallest multi-digit prime such that the product of digits is equal to the number of digits times the sum of the digits. I. e., 1×6×7 = 3×(1+6+7).

167 is a strictly non-palindromic number; that means its not palindromic in any base from binary to base 165. However, in base 10, 167 is a happy number, as the iteration of the digit-squaring procedure gives: 1^2 + 6^2 + 7^2 = 86, 8^2 + 6^2 = 100, and obviously 1^2 + 0^2 + 0^2 = 1. Another base 10 property of 167 is that it is a full reptend prime, since the decimal expansion of 1/167 repeats 0059880239520958083832335329341317365269461077844311377245508982035928143712574850299401197604790419161676646706586826347305389221556886227544910179640718562874251497 ad infinitam.

Uses

*The year 167
*In backgammon, a player needs a total of 167 pips to get all his pieces off the board, starting from the initial position.

External links

* [http://primes.utm.edu/curios/page.php/167.html prime curiosities: 167]