mingw-w32-bin_i686-mingw_.zip runs on and generates binaries for 32bit Windows (cf. The MinGW for Win64 project has also binaries for 32bit Windows e.g. Official MinGW builds (only releases), last seen was 6.3.0 ()
The file name pattern is - thus, mingw-w64-bin_x86_64-mingw_20100527.zip is a compiler targeting 64bit Windows ( mingw-w64) but also running ('host') on 64bit Windows ( xx86-64-mingw) you might search for the file in Toolchains targetting Win64 (Personal Builds or Automatized Builds). They provides several compilers, which run on Windows (32-bit and 64-bit Windows), Cygwin, Linux, and Darwin/MacOS - and which generate binaries for 32bit or 64bit Windows. MinGW for Win64: The Mingw-w64 project has regularly updated snapshots of compilers generating 64-bit Windows executables. If in doubt, or if you don't know what Cygwin and MinGW are, the package for you is the MinGW ('native Windows') package! Most of the builds below come from gfortran maintainers but not all.
Note: There do not exist any official FSF/GNU/GCC binary builds (only source packages). This page gathers links to all unofficial gfortran binary packages people regularly build, based on the current development gfortran source code.
