Long Period Prime/Examples/23
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Theorem
The prime number $23$ is a long period prime:
- $\dfrac 1 {23} = 0 \cdotp \dot 04347 \, 82608 \, 69565 \, 21739 \, 1 \dot 3$
This sequence is A021027 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Proof
From Reciprocal of $23$:
- $\dfrac 1 {23} = 0 \cdotp \dot 04347 \, 82608 \, 69565 \, 21739 \, 1 \dot 3$
Counting the digits, it is seen that this has a period of recurrence of $22$.
Hence the result.
$\blacksquare$
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $23$
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $0,434,782,608,695,652,173,913$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $23$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $0,434,782,608,695,652,173,913$