Long Period Prime/Examples/59
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Theorem
The prime number $59$ is a long period prime:
- $\dfrac 1 {59} = 0 \cdotp \dot 01694 \, 91525 \, 42372 \, 88135 \, 59322 \, 03389 \, 83050 \, 84745 \, 76271 \, 18644 \, 06779 \, 66 \dot 1$
Proof
From Reciprocal of $59$:
- $\dfrac 1 {59} = 0 \cdotp \dot 01694 \, 91525 \, 42372 \, 88135 \, 59322 \, 03389 \, 83050 \, 84745 \, 76271 \, 18644 \, 06779 \, 66 \dot 1$
Counting the digits, it is seen that this has a period of recurrence of $58$.
Hence the result.
$\blacksquare$