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The "Stealth Update" Bug. Even if you have SkyrimSE.exe set to 1.6.640, Steam might have downloaded the 1.6.1170 executable into a temporary folder. Or, a mod manager changed your root directory.
Fix:
You cannot find 1.6.640 SKSE on the front page of skse.silverlock.org. The main page always shows the latest build (currently for 1.6.1170).
To understand the significance of version 1.6.640, we must look at November 11, 2021.
Bethesda released The Elder Scrolls V: Skyrim Anniversary Edition to celebrate the game's 10th birthday. This was not just a simple patch; it was a significant backend update that upgraded the game from version 1.5.97 (the "Special Edition" standard for years) to version 1.6.317 (initial release), which was quickly followed by hotfixes, eventually culminating in the widely referenced 1.6.640 patch (released in early 2022 to fix the "black face" bug and other issues).
This update introduced "Creation Club" content integration and, crucially, updated the game's executable engine.
When people search for "skyrim+skse+16640+2021," they aren't just looking for the launcher. They want to know which mods from that era are compatible.