
theorem
  367 is prime
proof
  now
    367 = 2*183 + 1; hence not 2 divides 367 by NAT_4:9;
    367 = 3*122 + 1; hence not 3 divides 367 by NAT_4:9;
    367 = 5*73 + 2; hence not 5 divides 367 by NAT_4:9;
    367 = 7*52 + 3; hence not 7 divides 367 by NAT_4:9;
    367 = 11*33 + 4; hence not 11 divides 367 by NAT_4:9;
    367 = 13*28 + 3; hence not 13 divides 367 by NAT_4:9;
    367 = 17*21 + 10; hence not 17 divides 367 by NAT_4:9;
    367 = 19*19 + 6; hence not 19 divides 367 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 367 & n is prime
  holds not n divides 367 by XPRIMET1:16;
  hence thesis by NAT_4:14;
end;
