All about Palindrome Numbers

I am quite sure, that many of us know about 'palindrome' words – LEVEL, RADAR, MADAM, that can be read the same way in either direction. The same exists with numbers, just have a look at numbers: 878, 6886, 97679, 123321, 4345434
The above numbers remain same when their digits are reversed, such numbers are known as Palindromic Numbers or Number Palindromes and Prime Numbers that are palindrome are called as Palindromic Prime or Palprime. First few palprimes are - 2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 10301, 10501, 10601, 11311….

Apart from the digit pattern in the palindrome numbers, there are some other amazing facts of Palindrome Numbers as follows
1. All palprimes have odd number of digits except the number 11. ( from above list you can see that there are no 2 or 4 digit numbers)
2. Palindromes that have consecutive digits and even-highest middle digit are always divisible by 11 and the resultant quotient is also a palindrome. Ex.121 is divisible by 11 and quotient is 11 which is a palindrome. It has Even Highest Middile digit as 2.

121-(2)-11

1234321-(4)-112211

12345654321-(6)-1122332211

1223456787654321-(8)-11223344332211

3. Palindromes can be formed from a number that is not a palindrome. By adding the original non-palindrome number with the number formed by reversing the digits, we get a number that is palindrome either in one step or subsequent sets. This process is called as Lychrel Process. Example
One Step:
521 - Non Palindrome number
+ 125 - Reverse of Non Palindrome number
-------
646 - Palindrome !
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More than One Step:
529 - Non Palindrome number
+ 925 - Reverse of Non Palindrome number
---------
1454 - Non Palindrome
+ 4541 - Reverse of Non Palindrome number
---------
5995 - Palindrome !
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4. If a number cannot form a palindrome through the iterative process of repeatedly reversing the digits and adding the resulting numbers as mentioned above (step 3), then such a number is called as Lychrel Number. Till date no Lychrel numbers are known, though many numbers are suspected Lychrels, the smallest being 196. You can find more on Lychrel Numbers at http://en.wikipedia.org/wiki/Lychrel_number.

If you have any other cool facts about palindromes, do share.