
theorem
  487 is prime
proof
  now
    487 = 2*243 + 1; hence not 2 divides 487 by NAT_4:9;
    487 = 3*162 + 1; hence not 3 divides 487 by NAT_4:9;
    487 = 5*97 + 2; hence not 5 divides 487 by NAT_4:9;
    487 = 7*69 + 4; hence not 7 divides 487 by NAT_4:9;
    487 = 11*44 + 3; hence not 11 divides 487 by NAT_4:9;
    487 = 13*37 + 6; hence not 13 divides 487 by NAT_4:9;
    487 = 17*28 + 11; hence not 17 divides 487 by NAT_4:9;
    487 = 19*25 + 12; hence not 19 divides 487 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 487 & n is prime
  holds not n divides 487 by XPRIMET1:16;
  hence thesis by NAT_4:14;
end;
