Is notice from Prudential Financial Inc that you won a sweepstakes conducted electronically from the customer database of a group of consumer based companies legit or a scam?

Probably a scam. But by all means, let them mail you any check they like, then take it to the bank and see if it clears.

However, if they tell you of a small "fee" for taxes, processing or administrative costs - or anything else - do NOT do it!

No legitimate lottery has you pay to pick up the prize.