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1. INTRODUCTION. In the seventeenth century, Fermat defined the sequence of numbers F n = 2 2 n + 1 for n ≥ 0, now known as Fermat numbers. If F n happens to be prime, F n is called a Fermat prime. Fermat showed that F n is prime for each n ≤ 4, and he conjectured that F n is prime for all n (see Brown [1] or Burton [2, p. 271]). Almost one hundred years(More)