
theorem
  1997 is prime
proof
  now
    1997 = 2*998 + 1; hence not 2 divides 1997 by NAT_4:9;
    1997 = 3*665 + 2; hence not 3 divides 1997 by NAT_4:9;
    1997 = 5*399 + 2; hence not 5 divides 1997 by NAT_4:9;
    1997 = 7*285 + 2; hence not 7 divides 1997 by NAT_4:9;
    1997 = 11*181 + 6; hence not 11 divides 1997 by NAT_4:9;
    1997 = 13*153 + 8; hence not 13 divides 1997 by NAT_4:9;
    1997 = 17*117 + 8; hence not 17 divides 1997 by NAT_4:9;
    1997 = 19*105 + 2; hence not 19 divides 1997 by NAT_4:9;
    1997 = 23*86 + 19; hence not 23 divides 1997 by NAT_4:9;
    1997 = 29*68 + 25; hence not 29 divides 1997 by NAT_4:9;
    1997 = 31*64 + 13; hence not 31 divides 1997 by NAT_4:9;
    1997 = 37*53 + 36; hence not 37 divides 1997 by NAT_4:9;
    1997 = 41*48 + 29; hence not 41 divides 1997 by NAT_4:9;
    1997 = 43*46 + 19; hence not 43 divides 1997 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1997 & n is prime
  holds not n divides 1997 by XPRIMET1:28;
  hence thesis by NAT_4:14;
end;
