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Is there a possibility to run an open sesame experiment on a computer with only e-prime installed on it?
You cannot run an OpenSesame experiment in E-Prime, if that's what you're asking. However, you can easily download and run OpenSesame without requiring any installation (even straight from a USB stick). To do so, you can use the Windows XP/Vista/7 no installation required (.zip) or Windows XP/Vista/7 Python portable package (.zip) packages, provided on the download page:
There's much bigger issues in the world, I know. But I first have to take care of the world I know.