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The Primary Pretenders

J. H. Conway·R. K. Guy·W. A. Schneeberger·N. J. A. Sloane
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Abstract

We call a composite number q such that there exists a positive integer b with b^p == b (mod q) a prime pretender to base b. The least prime pretender to base b is the primary pretender q_b. It is shown that there are only 132 distinct primary pretenders, and that q_b is a periodic function of b whose period is the 122-digit number 19568584333460072587245340037736278982017213829337604336734362- 294738647777395483196097971852999259921329236506842360439300.

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BibTeXRIS

J. H. Conway, R. K. Guy, W. A. Schneeberger, N. J. A. Sloane. 2002-07-21. The Primary Pretenders. https://arxiv.org/abs/math/0207180

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