
theorem
  9719 is prime
proof
  now
    9719 = 2*4859 + 1; hence not 2 divides 9719 by NAT_4:9;
    9719 = 3*3239 + 2; hence not 3 divides 9719 by NAT_4:9;
    9719 = 5*1943 + 4; hence not 5 divides 9719 by NAT_4:9;
    9719 = 7*1388 + 3; hence not 7 divides 9719 by NAT_4:9;
    9719 = 11*883 + 6; hence not 11 divides 9719 by NAT_4:9;
    9719 = 13*747 + 8; hence not 13 divides 9719 by NAT_4:9;
    9719 = 17*571 + 12; hence not 17 divides 9719 by NAT_4:9;
    9719 = 19*511 + 10; hence not 19 divides 9719 by NAT_4:9;
    9719 = 23*422 + 13; hence not 23 divides 9719 by NAT_4:9;
    9719 = 29*335 + 4; hence not 29 divides 9719 by NAT_4:9;
    9719 = 31*313 + 16; hence not 31 divides 9719 by NAT_4:9;
    9719 = 37*262 + 25; hence not 37 divides 9719 by NAT_4:9;
    9719 = 41*237 + 2; hence not 41 divides 9719 by NAT_4:9;
    9719 = 43*226 + 1; hence not 43 divides 9719 by NAT_4:9;
    9719 = 47*206 + 37; hence not 47 divides 9719 by NAT_4:9;
    9719 = 53*183 + 20; hence not 53 divides 9719 by NAT_4:9;
    9719 = 59*164 + 43; hence not 59 divides 9719 by NAT_4:9;
    9719 = 61*159 + 20; hence not 61 divides 9719 by NAT_4:9;
    9719 = 67*145 + 4; hence not 67 divides 9719 by NAT_4:9;
    9719 = 71*136 + 63; hence not 71 divides 9719 by NAT_4:9;
    9719 = 73*133 + 10; hence not 73 divides 9719 by NAT_4:9;
    9719 = 79*123 + 2; hence not 79 divides 9719 by NAT_4:9;
    9719 = 83*117 + 8; hence not 83 divides 9719 by NAT_4:9;
    9719 = 89*109 + 18; hence not 89 divides 9719 by NAT_4:9;
    9719 = 97*100 + 19; hence not 97 divides 9719 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9719 & n is prime
  holds not n divides 9719 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
