Long Period Prime/Examples/17

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): $0,588,235,294,117,647$
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