Nov. 2, 2011 is a one-of-a-kind palindrome
Published: Wednesday, September 28, 2011
Updated: Monday, October 31, 2011 07:10
This year is special because it contains two palindrome calendar dates: Jan. 10, 2011 expressed as 1-10-2011 (or simply 1102011) and Nov. 2, 2011 written as 11-02-2011 (11022011). The first one has already occurred and the second one, 11022011, is coming up. (Note that in most of the world where day-month-year date format is used, this year also has two palindrome dates. Date 11022011 representing 11 February 2011 already passed and 1102011 corresponding to 1 October 2011 is about to occur.)
After 2011, there will be one more year in this (21st) century containing two palindrome dates. That will be 2021, with palindrome dates Jan. 20, 2021 (1202021) and Dec. 2, 2021 (12022021). (In the rest of the world, after 2011, there will also be one more year in this century containing two palindrome dates, but that year will be 2012 instead of 2021.)
Nov. 2, 2011 represented as 11022011 is a one-of-a-kind palindrome date with respect to all palindrome dates contained in all four-digit years. Why?
First, number 11022011 equals 7 x 7 x 11 x 11 x 11 x 13 x 13, that is, the product of seven square, eleven cube and thirteen square where numbers seven, eleven and thirteen are three consecutive prime numbers! So, number 11022011 is divisible by the product of the squares of three consecutive prime numbers! Furthermore, it's also divisible by the cube of the middle prime of the three consecutive primes! In fact, 11022011 = 72 x 113 x 132 where, interestingly enough, the three superscripts side-by-side constitute 232 which is also a palindrome! Fascinating, isn't it? No other such palindrome date exists in all four-digit years.
In addition, since 7 x 11 x 13 yields 1001, another palindrome number, one could also express date 11022011 as 1001 x 11 x 1001 where the left and right sides of this expression divided in the middle are almost mirror images of one another! Isn't that something?
Also, if date number 11022011 is split into four two-digit numbers as 11, 02, 20 and 11, the first two numbers add up to 13 and the sum of the last two is 31, and 13 and 31 put side-by-side yield 1331 = 11 x 11 x 11! Now, by introducing two zeros in-between the digits of the first and last elevens, this expression will change from 11 x 11 x 11 to 1001 x 11 x 1001 = 11022011! Wow!
I hope this article convinces you that the second palindrome date of this year 11022011 to occur in a little over a month is indeed special and unique compared to all other palindrome dates in four-digit years. And aren't we lucky that it is going to occur in our lifetime? Okay, you better hurry up and start the preparations now so you have all the arrangements in place to celebrate it fully when it occurs.
Aziz Inan is a professor of electrical engineering. He can be contacted at firstname.lastname@example.org.