let n be positive Nat; :: thesis: (8 * (2 |^ (2 |^ n))) + 1 is composite
H₁(8,n) >= (8 * 2) + 1 by Lm17;
hence H₁(8,n) >= 2 by XXREAL_0:2; :: according to NUMBER02:def 1 :: thesis: not (8 * (2 |^ (2 |^ n))) + 1 is prime
A1: (8 * (2 |^ (2 |^ n))) + 1 <> 3 by Lm17;
8 = (3 * 2) + 2 ;
hence not (8 * (2 |^ (2 |^ n))) + 1 is prime by A1, Th34; :: thesis: verum