Does anyone know what type of pepper plant this is?
After searching a little bit online, my guess would be Numex Twilight but I don't know enough about peppers to be sure. Can someone confirm? Or is it something else?
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It is difficult to be sure of the variety, but yes I would say it definitely looks like a Capsicum Fruescens cultivar.
Tabasco and Twilight are probably the two most common cultivars, and these are the two I've grown.
I'm going to lean towards Tabasco, because Twilight also ripens through yellows, oranges, and reds; in addition to purple. I'm not seeing this in your photo. See the photo on the Wikipedia page for an example of the colors.
Either way plant looks healthy. Personally I've probably had more success with Twilight but that might be 'luck' (seasons etc), they also look more colorful.