Problem Statement

A lot of composite numbers can be separated from primes by Fermat's Little Theorem, but there are some that completely confound it. The   Miller Rabin Test   uses a combination of Fermat's Little Theorem and Chinese Division Theorem to overcome this. The purpose of this task is to investigate such numbers using a method based on   Carmichael numbers,   as suggested in   Notes by G.J.O Jameson March 2010.

Find Carmichael numbers of the form: where   (Prime1 < Prime2 < Prime3)   for all   Prime1   up to   61. (See page 7 of   Notes by G.J.O Jameson March 2010   for solutions.)

For a given

P r i m

e

1

{\displaystyle Prime_{1}}

Chernick's Carmichael numbers

Let's start with the solution: