the exceptions listed above, has at least one primitive prime divisor. If n > 1, then the nth Pell number has at least one prime divisor that does not divide any earlier Pell number. The smallest primitive prime divisor of nth Pell number are 1, 2, 5, 3, 29, 7, 13, 17, 197, 41, 5741, 11, 33461, 239, 269, 577, 137, 199, 37, 19, 45697, 23, 229, 1153, 1549, 79, 53, 113, 44560482149, 31, 61, 665857, 52734529, 103, 1800193921, 73, 593, 9369319, 389, 241, ... See also Zsigmondy's theorem References . Fibonacci numbers Theorems in number theory