
theorem
  1033 is prime
proof
  now
    1033 = 2*516 + 1; hence not 2 divides 1033 by NAT_4:9;
    1033 = 3*344 + 1; hence not 3 divides 1033 by NAT_4:9;
    1033 = 5*206 + 3; hence not 5 divides 1033 by NAT_4:9;
    1033 = 7*147 + 4; hence not 7 divides 1033 by NAT_4:9;
    1033 = 11*93 + 10; hence not 11 divides 1033 by NAT_4:9;
    1033 = 13*79 + 6; hence not 13 divides 1033 by NAT_4:9;
    1033 = 17*60 + 13; hence not 17 divides 1033 by NAT_4:9;
    1033 = 19*54 + 7; hence not 19 divides 1033 by NAT_4:9;
    1033 = 23*44 + 21; hence not 23 divides 1033 by NAT_4:9;
    1033 = 29*35 + 18; hence not 29 divides 1033 by NAT_4:9;
    1033 = 31*33 + 10; hence not 31 divides 1033 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1033 & n is prime
  holds not n divides 1033 by XPRIMET1:22;
  hence thesis by NAT_4:14;
end;
