Long Period Prime/Examples/29
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Theorem
The prime number $29$ is a long period prime:
- $\dfrac 1 {29} = 0 \cdotp \dot 03448 \, 27586 \, 20689 \, 65517 \, 24137 \, 93 \dot 1$
This sequence is A021033 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Proof
From Reciprocal of $29$:
- $\dfrac 1 {29} = 0 \cdotp \dot 03448 \, 27586 \, 20689 \, 65517 \, 24137 \, 93 \dot 1$
Counting the digits, it is seen that this has a period of recurrence of $28$.
Hence the result.
$\blacksquare$