
theorem
  8753 is prime
proof
  now
    8753 = 2*4376 + 1; hence not 2 divides 8753 by NAT_4:9;
    8753 = 3*2917 + 2; hence not 3 divides 8753 by NAT_4:9;
    8753 = 5*1750 + 3; hence not 5 divides 8753 by NAT_4:9;
    8753 = 7*1250 + 3; hence not 7 divides 8753 by NAT_4:9;
    8753 = 11*795 + 8; hence not 11 divides 8753 by NAT_4:9;
    8753 = 13*673 + 4; hence not 13 divides 8753 by NAT_4:9;
    8753 = 17*514 + 15; hence not 17 divides 8753 by NAT_4:9;
    8753 = 19*460 + 13; hence not 19 divides 8753 by NAT_4:9;
    8753 = 23*380 + 13; hence not 23 divides 8753 by NAT_4:9;
    8753 = 29*301 + 24; hence not 29 divides 8753 by NAT_4:9;
    8753 = 31*282 + 11; hence not 31 divides 8753 by NAT_4:9;
    8753 = 37*236 + 21; hence not 37 divides 8753 by NAT_4:9;
    8753 = 41*213 + 20; hence not 41 divides 8753 by NAT_4:9;
    8753 = 43*203 + 24; hence not 43 divides 8753 by NAT_4:9;
    8753 = 47*186 + 11; hence not 47 divides 8753 by NAT_4:9;
    8753 = 53*165 + 8; hence not 53 divides 8753 by NAT_4:9;
    8753 = 59*148 + 21; hence not 59 divides 8753 by NAT_4:9;
    8753 = 61*143 + 30; hence not 61 divides 8753 by NAT_4:9;
    8753 = 67*130 + 43; hence not 67 divides 8753 by NAT_4:9;
    8753 = 71*123 + 20; hence not 71 divides 8753 by NAT_4:9;
    8753 = 73*119 + 66; hence not 73 divides 8753 by NAT_4:9;
    8753 = 79*110 + 63; hence not 79 divides 8753 by NAT_4:9;
    8753 = 83*105 + 38; hence not 83 divides 8753 by NAT_4:9;
    8753 = 89*98 + 31; hence not 89 divides 8753 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8753 & n is prime
  holds not n divides 8753 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
