Long Period Prime/Examples/17
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Theorem
The prime number $17$ is a long period prime:
- $\dfrac 1 {17} = 0 \cdotp \dot 05882 \, 35294 \, 11764 \, \dot 7$
Proof
From Reciprocal of $17$:
- $\dfrac 1 {17} = 0 \cdotp \dot 05882 \, 35294 \, 11764 \, \dot 7$
Counting the digits, it is seen that this has a period of recurrence of $16$.
Hence the result.
$\blacksquare$
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $17$
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $0,588,235,294,117,647$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $17$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $0,588,235,294,117,647$