Determine the number of sequences of positive integers $1 = x_0 < x_1 < \dots < x_{10} = 10^{5}$ with the property that for each $m=0,\dots,9$, the number $\frac{x_{m+1}}{x_m}$ is a prime number.

Let's think step by step and output the final answer within \boxed{}.
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