
theorem
  8779 is prime
proof
  now
    8779 = 2*4389 + 1; hence not 2 divides 8779 by NAT_4:9;
    8779 = 3*2926 + 1; hence not 3 divides 8779 by NAT_4:9;
    8779 = 5*1755 + 4; hence not 5 divides 8779 by NAT_4:9;
    8779 = 7*1254 + 1; hence not 7 divides 8779 by NAT_4:9;
    8779 = 11*798 + 1; hence not 11 divides 8779 by NAT_4:9;
    8779 = 13*675 + 4; hence not 13 divides 8779 by NAT_4:9;
    8779 = 17*516 + 7; hence not 17 divides 8779 by NAT_4:9;
    8779 = 19*462 + 1; hence not 19 divides 8779 by NAT_4:9;
    8779 = 23*381 + 16; hence not 23 divides 8779 by NAT_4:9;
    8779 = 29*302 + 21; hence not 29 divides 8779 by NAT_4:9;
    8779 = 31*283 + 6; hence not 31 divides 8779 by NAT_4:9;
    8779 = 37*237 + 10; hence not 37 divides 8779 by NAT_4:9;
    8779 = 41*214 + 5; hence not 41 divides 8779 by NAT_4:9;
    8779 = 43*204 + 7; hence not 43 divides 8779 by NAT_4:9;
    8779 = 47*186 + 37; hence not 47 divides 8779 by NAT_4:9;
    8779 = 53*165 + 34; hence not 53 divides 8779 by NAT_4:9;
    8779 = 59*148 + 47; hence not 59 divides 8779 by NAT_4:9;
    8779 = 61*143 + 56; hence not 61 divides 8779 by NAT_4:9;
    8779 = 67*131 + 2; hence not 67 divides 8779 by NAT_4:9;
    8779 = 71*123 + 46; hence not 71 divides 8779 by NAT_4:9;
    8779 = 73*120 + 19; hence not 73 divides 8779 by NAT_4:9;
    8779 = 79*111 + 10; hence not 79 divides 8779 by NAT_4:9;
    8779 = 83*105 + 64; hence not 83 divides 8779 by NAT_4:9;
    8779 = 89*98 + 57; hence not 89 divides 8779 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8779 & n is prime
  holds not n divides 8779 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
