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Prime divisors

I have a question about frequency of divisors. Lets say we have a number N, which the next lower number is prime, for example 48. One less than 48 is 47. 47 is a prime.

If I take 48 to a power. For example 48^2 is 2304. If I subtract 1 from this number it is 2303. One of the factors of 2303 is 47.

Why is it, that, no matter what power I use, for example 48^30=27367625686405765816997946520518481655117436 5773824 or another power and subtract 1, that one of the factors almost always, 47?

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