Recall Fermat's Little Theorem: For any prime p and integer a, ap−1≡mod p It happens that the converse to FLT is often but not always true. That is, if n is composite and a is an integer, then more often than not a^(n-1)≢1 mod n We can use this as the basis of a simple primality test, called the Fermat Test. For a∈Zn  we make the following definitions. 1) We call   a a Fermat Liar for n if a^(n−1)≡1 mod n  , where a∉(0,1,n−1) 2) We call a a Fermat Witness for n if a^(n−1)≢1modn  where a∉(0,1,n−1) If a number is composite, then 2 is very often a Fermat Witness. What is the smallest composite integer n greater than 72697269 for which 2 is not a Fermat Witness?

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