
theorem
  1993 is prime
proof
  now
    1993 = 2*996 + 1; hence not 2 divides 1993 by NAT_4:9;
    1993 = 3*664 + 1; hence not 3 divides 1993 by NAT_4:9;
    1993 = 5*398 + 3; hence not 5 divides 1993 by NAT_4:9;
    1993 = 7*284 + 5; hence not 7 divides 1993 by NAT_4:9;
    1993 = 11*181 + 2; hence not 11 divides 1993 by NAT_4:9;
    1993 = 13*153 + 4; hence not 13 divides 1993 by NAT_4:9;
    1993 = 17*117 + 4; hence not 17 divides 1993 by NAT_4:9;
    1993 = 19*104 + 17; hence not 19 divides 1993 by NAT_4:9;
    1993 = 23*86 + 15; hence not 23 divides 1993 by NAT_4:9;
    1993 = 29*68 + 21; hence not 29 divides 1993 by NAT_4:9;
    1993 = 31*64 + 9; hence not 31 divides 1993 by NAT_4:9;
    1993 = 37*53 + 32; hence not 37 divides 1993 by NAT_4:9;
    1993 = 41*48 + 25; hence not 41 divides 1993 by NAT_4:9;
    1993 = 43*46 + 15; hence not 43 divides 1993 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1993 & n is prime
  holds not n divides 1993 by XPRIMET1:28;
  hence thesis by NAT_4:14;
end;
