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The Minix website says nothing about the Y2038 problem.
Does Minix impliment the moderized POSIX time system calls?
Is Minix internally immune to the Y2038 problem?
People are using the kernal in embedded OSes, so this is important.
I assume the current Minix file system is immune to the problem, but most
people probably use ReiserFS (that I assume is immune).
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What is the Year 2038 problem?
http://computer.howstuffworks.com/question75.htm

The Year 2000 problem is understood by most people these days because of the
large amount of media attention it received.

Most programs written in the C programming language are relatively immune to
the Y2K problem, but suffer instead from the Year 2038 problem. This problem
arises because most C programs use a library of routines called the standard
time library . This library establishes a standard 4-byte format for the
storage of time values, and also provides a number of functions for
converting, displaying and calculating time values.

The standard 4-byte format assumes that the beginning of time is January 1,
1970, at 12:00:00 a.m. This value is 0. Any time/date value is expressed as
the number of seconds following that zero value. So the value 919642718 is
919,642,718 seconds past 12:00:00 a.m. on January 1, 1970, which is Sunday,
February 21, 1999, at 16:18:38 Pacific time (U.S.). This is a convenient
format because if you subtract any two values, what you get is a number of
seconds that is the time difference between them. Then you can use other
functions in the library to determine how many
minutes/hours/days/months/years have passed between the two times.

If you have read "How Bits and Bytes Work", you know that a signed 4-byte
integer has a maximum value of 2,147,483,647, and this is where the Year
2038 problem comes from. The maximum value of time before it rolls over to a
negative (and invalid) value is 2,147,483,647, which translates into January
19, 2038. On this date, any C programs that use the standard time library
will start to have problems with date calculations.

This problem is somewhat easier to fix than the Y2K problem on mainframes.
Well-written programs can simply be recompiled with a new version of the
library that uses, for example, 8-byte values for the storage format. This
is possible because the library encapsulates the whole time activity with
its own time types and functions (unlike most mainframe programs, which did
not standardize their date formats or calculations). So the Year 2038
problem should not be nearly as hard to fix as the Y2K problem was.