The palindromic number conjecture asserts that repeatedly reversing the decimal digits of a positive integer and adding the result to the original number eventually produces a palindromic number. This process is the 196-algorithm (Gardner 1979). Among the positive integers below 10000, 248 do not produce a palindromic number within 23 reverse-and-add steps.
The generalization to other bases has been refuted for bases that are a power of 2. The decimal conjecture remains open. Among the first 100000 numbers, Gruenberger (1984) reported 5996 candidates that had not generated a palindromic number. This finite computation does not prove that they never do so. The trajectory starting at 196 begins 196, 887, 1675, 7436, 13783, 52514, 94039, 187088, 1067869, 10755470, ... (OEIS A006960).
It is also conjectured that there are infinitely many palindromic primes. With the exception of 11, palindromic primes must have an odd number of digits.
