
theorem
  1663 is prime
proof
  now
    1663 = 2*831 + 1; hence not 2 divides 1663 by NAT_4:9;
    1663 = 3*554 + 1; hence not 3 divides 1663 by NAT_4:9;
    1663 = 5*332 + 3; hence not 5 divides 1663 by NAT_4:9;
    1663 = 7*237 + 4; hence not 7 divides 1663 by NAT_4:9;
    1663 = 11*151 + 2; hence not 11 divides 1663 by NAT_4:9;
    1663 = 13*127 + 12; hence not 13 divides 1663 by NAT_4:9;
    1663 = 17*97 + 14; hence not 17 divides 1663 by NAT_4:9;
    1663 = 19*87 + 10; hence not 19 divides 1663 by NAT_4:9;
    1663 = 23*72 + 7; hence not 23 divides 1663 by NAT_4:9;
    1663 = 29*57 + 10; hence not 29 divides 1663 by NAT_4:9;
    1663 = 31*53 + 20; hence not 31 divides 1663 by NAT_4:9;
    1663 = 37*44 + 35; hence not 37 divides 1663 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1663 & n is prime
  holds not n divides 1663 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
