Does it take the same amount of BP to prestige? (Cosmetics)

There's some characters I don't main but occasionally use to change things up. I like prestiging them for the bloody cosmetics when I can, but now thats going to be levels 4, 5, 6 instead of 1, 2, 3? Basically double the BP grind? This is severely punishing for the those of us who just want the bloody cosmetic..

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