Of my 3 characters, one never receives the Prime Attunement buff, and my other two, never lose it regardless of how many drop. Also, I've had some "wealth of the emperor" buffs for a few months now, it seems they stopped working once i completed the chalice. Initially prime attunement would wear off after dropping 2 prime engrams, like normal, but it got this way after a time playing.
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I believe you need to complete the forsaken campaign and speak to rahool to get your first prime after that the buff starts. The prime attunement buff stacks I think is 2 or 3 a day and stacks up to 9. The numbers keep changing. Meaning if you’re capped out it won’t go away until you get 9 in that day.