Is there a proof that shows that for any power of 10 the largest palindrome formed by the product of two numbers with equal number of digits occur in the last tenth of the given power of ten. Or another way to say it is do the two numbers start with 9.
First 6 examples
99*91=9009 993*913=906609 9999*9901=99000099 99979*99681=9966006699 999999*999001=999000000999 9999979*9467731=94677111177649
Also is possible to show that the palindrome has to start with a 9? This may be two separate questions but they seem closely related.
Also, if your wondering where I came up with this I was working on project 4 of the Euler project http://projecteuler.net/problem=4 and after solving the problem and then generalizing the problem to all powers of ten I was wondering how to optimize my algorithm to search for these palindromes.