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High Quality Content by WIKIPEDIA articles! In number theory, Zsigmondy's theorem states that if a b 0 are coprime integers, then for any natural number n 1 there is a prime number p (called a primitive prime divisor) that divides an bn and does not divide ak bk for any positive integer k 1 and n is not equal to 6, then 2n-1 has a prime divisor not dividing any 2k-1 with kn.