
theorem
  2803 is prime
proof
  now
    2803 = 2*1401 + 1; hence not 2 divides 2803 by NAT_4:9;
    2803 = 3*934 + 1; hence not 3 divides 2803 by NAT_4:9;
    2803 = 5*560 + 3; hence not 5 divides 2803 by NAT_4:9;
    2803 = 7*400 + 3; hence not 7 divides 2803 by NAT_4:9;
    2803 = 11*254 + 9; hence not 11 divides 2803 by NAT_4:9;
    2803 = 13*215 + 8; hence not 13 divides 2803 by NAT_4:9;
    2803 = 17*164 + 15; hence not 17 divides 2803 by NAT_4:9;
    2803 = 19*147 + 10; hence not 19 divides 2803 by NAT_4:9;
    2803 = 23*121 + 20; hence not 23 divides 2803 by NAT_4:9;
    2803 = 29*96 + 19; hence not 29 divides 2803 by NAT_4:9;
    2803 = 31*90 + 13; hence not 31 divides 2803 by NAT_4:9;
    2803 = 37*75 + 28; hence not 37 divides 2803 by NAT_4:9;
    2803 = 41*68 + 15; hence not 41 divides 2803 by NAT_4:9;
    2803 = 43*65 + 8; hence not 43 divides 2803 by NAT_4:9;
    2803 = 47*59 + 30; hence not 47 divides 2803 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2803 & n is prime
  holds not n divides 2803 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
