The latest it can fall is April 25, which happened in 1943 and will occur again in 2038.
2038 also happens to be when, on January 19 at 03:14:08 UTC (the evening of the 18th here in Eastern US), the Unix operating system date/time, using the POSIX system, will "wrap around" back to what represents December 13, 1901.
There is thought that this might require efforts similar to those taken to avert problems when January 1, 2000 came around. Though many think there wasn't a problem back then, it only appeared that way due to the tremendous coordinated efforts of thousands of people coding, testing, and monitoring systems around the world. I can attest to the hard work required!
Let's hope 2038 passes smoothly, as I will be 87 in January that year (if I'm still around, of course), and hope that I won't be hooked up to some machine that decides to fail...
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