I apologize to the world for my stupid American units, but the 5 gallon buckets are very good options to house a full grown plant. Peppers generally like taller lengthier pots as opposed to short wide pots.
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Now that being said, you can grow a pepper plant in about anything. I have a few bonsai'ing in as small as 3 inch seedling pots. They are putting out peppers and everything. Very happy. But I have to take a lot more care of them as they will suck up water and nutes very fast in such a small pot. The plants also do not get as big, which is what I want for the bonsai situation. But if you want big plants and lots of fruit, use big (and deep) pots.
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I generally start my plants in 3 inch pots, then up-pot seedlings to a #1 (approx. 2 liters?) pot and let the roots fill it up. Then I up-pot to the final pot, whether that be a #2 (approx 1.5 gallons), #3 (approx. 3 gallons), or a 5 gallon bucket that I buy from a hardware store and poke holes in.
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Simple answer, I am sure more people will chime in.
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PS: I did, however, grow a Trinidad Moruga Scorpion in a 20 gallon pot once and the plant itself from soil level was over 7 feet tall and 7 feet wide! HUNDREDS of pods.