reserve a,b,c,k,m,n for Nat;
reserve i,j for Integer;
reserve p for Prime;

theorem Th37:
  for n being positive Nat holds 8 * 2|^(2|^n) + 1 is composite
  proof
    let n be positive Nat;
    F(8,n) >= 8*2+1 by Lm17;
    hence F(8,n) >= 2 by XXREAL_0:2;
A1: 8*2|^(2|^n) + 1 <> 3 by Lm17;
    8 = 3*2+2;
    hence thesis by A1,Th34;
  end;
