103 is Smallest Prime whose Period of Reciprocal is One Third of Maximal

Theorem
$103$ is the smallest prime number the period of whose decimal expansion of its reciprocal is $\dfrac 1 3$ of its maximum length, that is: $34$:
 * $\dfrac 1 {103} = 0 \cdotp \dot 00970 \, 87378 \, 64077 \, 66990 \, 29126 \, 21359 \, 223 \dot 3$

Proof
Performing the calculation using long division:

0.0097087378640776699029126213592233009... 103)1.0000000000000000000000000000000000000...     927     618     927     103    309      ---     ---     ---     ---    ---       730     420      300    370     1000       721     412      206    309      927       ---     ---      ---    ---              900     800     940    610    ....         824     721     927    515         ---     ---     ---    ---          760     790     130    950          721     721     103    927          ---     ---     ---    ---           390     690     270    230           309     618     206    206           ---     ---     ---    ---            810     720     640    240            721     618     618    206            ---     ---     ---    ---             890    1020     220    340             824     927     206    309             ---         ---    ---              660     930     140    310              618     927     103    309