Long Period Prime/Examples/59

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.

$\blacksquare$