# 277

This number is a prime.

Single Curio View: (Seek other curios for this number)

A primary pretender for the base *b*is the smallest composite number

*n*for which

*b*

^{n}≡

*b*(mod

*n*). The list of these (when

*b*= 0, 1, 2, ...) begins 4, 4, 341, 6, 4, 4, 6, 6, 4, 4, 6, 10, 4, 4, 14, 6, 4, 4, 6, 6, 4, 4, 6, 22, 4, 4, 9, 6, 4, 4, 6, 6, 4, 4, 6, 9, ... Do you see the pattern yet? There are only 132 distinct numbers that appear in this list, but it repeats with a period of length 277#*23#. (Take a moment and calculate how large that period is!) [CGSS1997]

Submitted: 2008-03-10 21:04:14; Last Modified: 2008-08-02 16:07:00.

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