Learn Farsi: سه هفته است که یک همدم دارم. - I have had a companion for three weeks.

In Farsi, when an action or state started in the past and is still continuing right now, you use the present tense. Because you still have this companion, dâram (I have) is used instead of a past tense verb. The structure ast ke acts like a bridge connecting the past duration (three weeks) to the current ongoing state.

Can I literally translate "for three weeks" instead of using se hafte ast ke?

You could use a preposition like barâye (for) or be moddat-e (for the duration of) in some contexts, but using a time expression followed by ast ke and a present tense verb is the most natural, native-sounding way to express "I have been doing X for Y amount of time" in Farsi. Literally, this sentence translates to "It is three weeks that I have a companion."

I noticed dâram doesn't have the mi- prefix. Shouldn't it be mi-dâram to show ongoing present tense?

That is a great thing to watch out for! The verb dâshtan (to have) is an exception. It describes a state of being rather than a continuous action, so it never takes the mi- prefix in the simple present tense. You always just say dâram, never mi-dâram.

What is the literal meaning of the word hamdam?

Hamdam translates to "companion" or "close friend," but its literal breakdown is very poetic. It is made of ham (same or together) and (breath). So a is someone who breathes the same breath as you, implying a very close, intimate bond.