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

theorem Th35:
  for n being positive Nat holds 2 * 2|^(2|^n) + 1 is composite
  proof
    let n be positive Nat;
    F(2,n) >= 2*2+1 by Lm15;
    hence F(2,n) >= 2 by XXREAL_0:2;
    2 * 2|^(2|^n) + 1 <> 3;
    hence thesis by Lm13;
  end;
