Am I going to die?

Discrete Mathematics Level pending

I was rushing through the rooms, away from a vicious monster. In each room, there are a different number of doors but only one door leads to the right way while the others lead to a dead end. The first room has 4 doors. The second room has one door more than the first. The third room has one door more than the second room. This continues for ten rooms until I am finally free. The probability that I will choose the right room all the time is 1 in x. Find the number of (distinct) prime factors that x has.

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