
theorem
  8803 is prime
proof
  now
    8803 = 2*4401 + 1; hence not 2 divides 8803 by NAT_4:9;
    8803 = 3*2934 + 1; hence not 3 divides 8803 by NAT_4:9;
    8803 = 5*1760 + 3; hence not 5 divides 8803 by NAT_4:9;
    8803 = 7*1257 + 4; hence not 7 divides 8803 by NAT_4:9;
    8803 = 11*800 + 3; hence not 11 divides 8803 by NAT_4:9;
    8803 = 13*677 + 2; hence not 13 divides 8803 by NAT_4:9;
    8803 = 17*517 + 14; hence not 17 divides 8803 by NAT_4:9;
    8803 = 19*463 + 6; hence not 19 divides 8803 by NAT_4:9;
    8803 = 23*382 + 17; hence not 23 divides 8803 by NAT_4:9;
    8803 = 29*303 + 16; hence not 29 divides 8803 by NAT_4:9;
    8803 = 31*283 + 30; hence not 31 divides 8803 by NAT_4:9;
    8803 = 37*237 + 34; hence not 37 divides 8803 by NAT_4:9;
    8803 = 41*214 + 29; hence not 41 divides 8803 by NAT_4:9;
    8803 = 43*204 + 31; hence not 43 divides 8803 by NAT_4:9;
    8803 = 47*187 + 14; hence not 47 divides 8803 by NAT_4:9;
    8803 = 53*166 + 5; hence not 53 divides 8803 by NAT_4:9;
    8803 = 59*149 + 12; hence not 59 divides 8803 by NAT_4:9;
    8803 = 61*144 + 19; hence not 61 divides 8803 by NAT_4:9;
    8803 = 67*131 + 26; hence not 67 divides 8803 by NAT_4:9;
    8803 = 71*123 + 70; hence not 71 divides 8803 by NAT_4:9;
    8803 = 73*120 + 43; hence not 73 divides 8803 by NAT_4:9;
    8803 = 79*111 + 34; hence not 79 divides 8803 by NAT_4:9;
    8803 = 83*106 + 5; hence not 83 divides 8803 by NAT_4:9;
    8803 = 89*98 + 81; hence not 89 divides 8803 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8803 & n is prime
  holds not n divides 8803 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
