
theorem
  137 is prime
proof
  now
    137 = 2*68 + 1; hence not 2 divides 137 by NAT_4:9;
    137 = 3*45 + 2; hence not 3 divides 137 by NAT_4:9;
    137 = 5*27 + 2; hence not 5 divides 137 by NAT_4:9;
    137 = 7*19 + 4; hence not 7 divides 137 by NAT_4:9;
    137 = 11*12 + 5; hence not 11 divides 137 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 137 & n is prime
  holds not n divides 137 by XPRIMET1:10;
  hence thesis by NAT_4:14;
end;
