Year 2038 problem
The biggest number you can store this way is 2,147,483,647 seconds after 1 January 1970.  This means 19th January 2038 at 03:14:07 UTC.  The problem begins one second after this time.  The computer will add 1 to this 32-bit number, and the computer will set the value to negative 2,147,483,648 seconds.  This means 13th December 1901 at 20:45:52 UTC.  Depending on how the computer has been programmed, the computer could behave incorrectly or even stop running.