Period of Reciprocal of Repunit 1031 is 1031

Theorem
The decimal expansion of the reciprocal of the repunit prime $R1031$ has a period of $1031$.
 * $\dfrac 1 {R1031} = 0 \cdotp \underbrace{\dot 000 \ldots 000}_{1030} \dot 9$

This is the only prime number to have a period of exactly $1031$.

Proof
The reciprocal of a repunit $R_n$ is of the form:
 * $\dfrac 1 {Rn} = 0 \cdotp \underbrace{\dot 000 \ldots 000}_{n - 1} \dot 9$

Thus $\dfrac 1 {R1031}$ has a period of $1031$.