Period of Reciprocal of 23 is of Maximal Length

Theorem
The decimal expansion of the reciprocal of $19$ has the maximum period, that is: $22$:
 * $\dfrac 1 {23} = 0 \cdotp \dot 04347 \, 82608 \, 69565 \, 21739 \, 1 \dot 3$

Proof
Performing the calculation using long division:

0.043478260869565217391304... - 23)1.00000000000000000000000000     92     184     23     --     ---     --      80     160    170      69     138    161      --     ---    ---      110     220     90       92     207     69      ---     ---     --       180     130    210       161     115    207       ---     ---    ---        190     150     30        184     138     23        ---     ---     --          60     120     70          46     115     69          --     ---     --          140      50     100          138      46      92          ---      --     ---            200     40    ...            184     23