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Автор

It should be 99=11*3*3...
The right side 10^n-1 is always divisible with 9 and result larger than one, then left side multiplied by that result is not prime certainly. But for divisible by 11 it is either left or right side and always result is larger than one.
It looks like non-prime generator for n>=2.

jarikosonen
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I didn't understand the final step

rafael
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10101 is divisible by 37 because 101 + 10 = 111 = 3 * 37

michaelempeigne