Prime Curios!: 277

277
(another Prime Pages' Curiosity)

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A primary pretender for the base b is the smallest composite number n for which bⁿ

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 16:04:14; Last Modified: 2008-08-02 11:07:00.