When looking up other things on the internet, I came across the number 167 on wikipedia and was really shocked to see how important this number really is and how it relates to so much in our math class. I used to think that 167 was just a number between 166 and 168, but not anymore =)
* 167 is an odd number
* 167 is a Chen prime, since the next odd number, 169, is a square of a prime
* 167 is an Eisenstein prime with no imaginary part and a real part of the form 3n − 1
* 167 is a full reptend prime in base 10, since the decimal expansion of 1/167 repeats to infinity
* 167 is a Gaussian prime number
* 167 is a happy number in base 10, 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
* 167 is a highly cototient number, as it is the smallest number k with exactly 15 solutions to the equation x - φ(x) = k
* 167 is a safe prime
* 167 is a strictly non-palindromic number; thus its not palindromic in any base from binary to base 165
* 167 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)
Can anyone else find numbers out there that are that relevant? I'm sure it's possible!
