A primary language is that which is dominant at the time. Example: at home you might speak Russian. Russian might be your First language - the one you learned as a baby.
At work, at an international company with lots of expats, the primary language might be English, as it is the lingua franca used between coworkers.
the terms L1 and L2 are used to define first and second languages. There are no Third or L3 languages. You can have more than one L1 if you are raised bilingual for example. Many people have more than one L2 - My L2s are German and Russian, fro example.