Long Period Prime/Examples/23

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