Long Period Prime/Examples/47

Theorem

The prime number $47$ is a long period prime:

$\dfrac 1 {47} = 0 \cdotp \dot 02127 \, 65957 \, 44680 \, 85106 \, 38297 \, 87234 \, 04255 \, 31914 \, 89361 \, \dot 7$

Proof

From Reciprocal of $47$:

$\dfrac 1 {47} = 0 \cdotp \dot 02127 \, 65957 \, 44680 \, 85106 \, 38297 \, 87234 \, 04255 \, 31914 \, 89361 \, \dot 7$

Counting the digits, it is seen that this has a period of recurrence of $46$.

Hence the result.

$\blacksquare$