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Like issue31882, this is to mention an upstream bug in Cygwin that causes one of the tests in the test_socket test suite to hang indefinitely. That bug is fixed upstream [1], but for now it would still be better to skip the test on Cygwin.
The bug is that in some cases a blocking send() (particularly for a large amount data) cannot be interrupted by a signal even if SA_RESTART is not set.
Fixes to this issue, along with issue31882, issue31883, and issue31878 provide the bare minimum for Cygwin to at least compile (not necessarily all optional extension modules) and run the test suite from start to finish (though there may be other tests that cause the interpreter to lock up, but that are currently masked by other bugs).
[1] https://cygwin.com/ml/cygwin-patches/2017-q2/msg00037.html 

Erik, is this still relevant, given the Cygwin bug was fixed 4 years ago?

Thanks for asking. Indeed the fix to that issue was included in https://cygwin.com/git/?p=newlib-cygwin.git;a=commit;h=5ca286666a0cd71436a84797d5d66831790004e0 and as Cygwin obsoletes old releases rather quickly I see no reason to keep this issue open.

Thanks. Do you know whether anyone is looking at Cygwin support for cpython at the moment? Is there interest in that?

That person was me--I have the keys to a cygwin buildbot, but it's currently not running. I lost the urgency to make cygwin fully supported, though it's come a long way. In particular the deprecation of distutils should help nix some of the long-standing issues.