Long Period Prime/Examples/47
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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.
$\blacksquare$