
theorem
  8807 is prime
proof
  now
    8807 = 2*4403 + 1; hence not 2 divides 8807 by NAT_4:9;
    8807 = 3*2935 + 2; hence not 3 divides 8807 by NAT_4:9;
    8807 = 5*1761 + 2; hence not 5 divides 8807 by NAT_4:9;
    8807 = 7*1258 + 1; hence not 7 divides 8807 by NAT_4:9;
    8807 = 11*800 + 7; hence not 11 divides 8807 by NAT_4:9;
    8807 = 13*677 + 6; hence not 13 divides 8807 by NAT_4:9;
    8807 = 17*518 + 1; hence not 17 divides 8807 by NAT_4:9;
    8807 = 19*463 + 10; hence not 19 divides 8807 by NAT_4:9;
    8807 = 23*382 + 21; hence not 23 divides 8807 by NAT_4:9;
    8807 = 29*303 + 20; hence not 29 divides 8807 by NAT_4:9;
    8807 = 31*284 + 3; hence not 31 divides 8807 by NAT_4:9;
    8807 = 37*238 + 1; hence not 37 divides 8807 by NAT_4:9;
    8807 = 41*214 + 33; hence not 41 divides 8807 by NAT_4:9;
    8807 = 43*204 + 35; hence not 43 divides 8807 by NAT_4:9;
    8807 = 47*187 + 18; hence not 47 divides 8807 by NAT_4:9;
    8807 = 53*166 + 9; hence not 53 divides 8807 by NAT_4:9;
    8807 = 59*149 + 16; hence not 59 divides 8807 by NAT_4:9;
    8807 = 61*144 + 23; hence not 61 divides 8807 by NAT_4:9;
    8807 = 67*131 + 30; hence not 67 divides 8807 by NAT_4:9;
    8807 = 71*124 + 3; hence not 71 divides 8807 by NAT_4:9;
    8807 = 73*120 + 47; hence not 73 divides 8807 by NAT_4:9;
    8807 = 79*111 + 38; hence not 79 divides 8807 by NAT_4:9;
    8807 = 83*106 + 9; hence not 83 divides 8807 by NAT_4:9;
    8807 = 89*98 + 85; hence not 89 divides 8807 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8807 & n is prime
  holds not n divides 8807 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
