last version mirror of cygwin which supports Windows XP: Cygwin version: 25 Aug 2016 ('30 Aug' dump is coming). Setup version: 2.874
Download from:
http://cygwin-xp.portfolis.net/
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Download setup version 2.874 directly from the Cygwin Time Machine.
http://ctm.crouchingtigerhiddenfruitbat.org/pub/cygwin/setup/snapshots/setup-x86-2.874.exe
http://ctm.crouchingtigerhiddenfruitbat.org/pub/cygwin/setup/snapshots/setup-x86_64-2.874.exe
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Create a shortcut with the -X parameter to disable signature checking. Right click the .exe and select "Copy". Right click on the desktop or in a directory and select "paste as short cut". Right click the shortcut you just created and select properties. Select the "Shortcut" tab. Add " -X" (without quotes) to the end of the target field. Click OK to save the change.
execute (double click) the shortcut and install cygwin. When you reach Choose a Download Site , enter a URL from below in the User URL field and click ADD.
http://ctm.crouchingtigerhiddenfruitbat.org/pub/cygwin/circa/2016/08/30/104223
http://ctm.crouchingtigerhiddenfruitbat.org/pub/cygwin/circa/64bit/2016/08/30/104235
Scroll through the list of Avaiable Download Sites and make sure that www.fruitbat.org is the only one highlighted . The full URL you entered won't be displayed, you have to take it on faith that the correct mirror date will be remembered and used. Finally, you can click Next.
Whenever you want to do maintenance, always use this shortcut.
Prepare for bad things by saving a copy of cygwin1.dll (found in /cygwin/bin, a sub-directory of your install directory.) Do this using windows, and store it outside C:\cygwin.
OBS: Cygwin Mirrors are out to get you. Mirrors other than Fruitbat are constantly being upgraded, and do not preserve the older setup.ini files. At best, only the most previous version of an upgraded package is preserved.