theorem
  201 satisfies_Sierpinski_problem_89
  proof
    set n = 201;
    thus n is_a_product_of_two_different_primes
    proof
      take P3,P67;
      thus thesis;
    end;
    thus n+1 is_a_product_of_two_different_primes
    proof
      take P2,P101;
      thus thesis;
    end;
    thus n+2 is_a_product_of_two_different_primes
    proof
      take P7,P29;
      thus thesis;
    end;
  end;
