
theorem
  3203 is prime
proof
  now
    3203 = 2*1601 + 1; hence not 2 divides 3203 by NAT_4:9;
    3203 = 3*1067 + 2; hence not 3 divides 3203 by NAT_4:9;
    3203 = 5*640 + 3; hence not 5 divides 3203 by NAT_4:9;
    3203 = 7*457 + 4; hence not 7 divides 3203 by NAT_4:9;
    3203 = 11*291 + 2; hence not 11 divides 3203 by NAT_4:9;
    3203 = 13*246 + 5; hence not 13 divides 3203 by NAT_4:9;
    3203 = 17*188 + 7; hence not 17 divides 3203 by NAT_4:9;
    3203 = 19*168 + 11; hence not 19 divides 3203 by NAT_4:9;
    3203 = 23*139 + 6; hence not 23 divides 3203 by NAT_4:9;
    3203 = 29*110 + 13; hence not 29 divides 3203 by NAT_4:9;
    3203 = 31*103 + 10; hence not 31 divides 3203 by NAT_4:9;
    3203 = 37*86 + 21; hence not 37 divides 3203 by NAT_4:9;
    3203 = 41*78 + 5; hence not 41 divides 3203 by NAT_4:9;
    3203 = 43*74 + 21; hence not 43 divides 3203 by NAT_4:9;
    3203 = 47*68 + 7; hence not 47 divides 3203 by NAT_4:9;
    3203 = 53*60 + 23; hence not 53 divides 3203 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3203 & n is prime
  holds not n divides 3203 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
