
theorem
  8387 is prime
proof
  now
    8387 = 2*4193 + 1; hence not 2 divides 8387 by NAT_4:9;
    8387 = 3*2795 + 2; hence not 3 divides 8387 by NAT_4:9;
    8387 = 5*1677 + 2; hence not 5 divides 8387 by NAT_4:9;
    8387 = 7*1198 + 1; hence not 7 divides 8387 by NAT_4:9;
    8387 = 11*762 + 5; hence not 11 divides 8387 by NAT_4:9;
    8387 = 13*645 + 2; hence not 13 divides 8387 by NAT_4:9;
    8387 = 17*493 + 6; hence not 17 divides 8387 by NAT_4:9;
    8387 = 19*441 + 8; hence not 19 divides 8387 by NAT_4:9;
    8387 = 23*364 + 15; hence not 23 divides 8387 by NAT_4:9;
    8387 = 29*289 + 6; hence not 29 divides 8387 by NAT_4:9;
    8387 = 31*270 + 17; hence not 31 divides 8387 by NAT_4:9;
    8387 = 37*226 + 25; hence not 37 divides 8387 by NAT_4:9;
    8387 = 41*204 + 23; hence not 41 divides 8387 by NAT_4:9;
    8387 = 43*195 + 2; hence not 43 divides 8387 by NAT_4:9;
    8387 = 47*178 + 21; hence not 47 divides 8387 by NAT_4:9;
    8387 = 53*158 + 13; hence not 53 divides 8387 by NAT_4:9;
    8387 = 59*142 + 9; hence not 59 divides 8387 by NAT_4:9;
    8387 = 61*137 + 30; hence not 61 divides 8387 by NAT_4:9;
    8387 = 67*125 + 12; hence not 67 divides 8387 by NAT_4:9;
    8387 = 71*118 + 9; hence not 71 divides 8387 by NAT_4:9;
    8387 = 73*114 + 65; hence not 73 divides 8387 by NAT_4:9;
    8387 = 79*106 + 13; hence not 79 divides 8387 by NAT_4:9;
    8387 = 83*101 + 4; hence not 83 divides 8387 by NAT_4:9;
    8387 = 89*94 + 21; hence not 89 divides 8387 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8387 & n is prime
  holds not n divides 8387 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
