The Primary Pretenders
  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. 
J. H. Conway, R. K. Guy, W. A. Schneeberger, N. J. A. Sloane