Apply the 196-algorithm, which consists of taking any positive integer of two digits or more, reversing
the digits, and adding to the original number. Now sum the two and repeat the procedure
with the sum. Of the first 
numbers, only 251 do not produce a palindromic
number in 
steps (Gardner 1979).
It was therefore conjectured that all numbers will eventually yield a palindromic number. However, the conjecture has been proven false for bases which are a power of 2, and seems to be false for base 10 as well. Among
the first 
numbers, 
numbers apparently never generate a palindromic
number (Gruenberger 1984). The first few are 196, 887, 1675, 7436, 13783, 52514,
94039, 187088, 1067869, 10755470, ... (OEIS A006960).
It is conjectured, but not proven, that there are an infinite number of palindromic primes. With the exception of 11, palindromic primes must have an odd number of digits.
