Long Period Prime/Examples/29

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.

$\blacksquare$