
theorem
  8893 is prime
proof
  now
    8893 = 2*4446 + 1; hence not 2 divides 8893 by NAT_4:9;
    8893 = 3*2964 + 1; hence not 3 divides 8893 by NAT_4:9;
    8893 = 5*1778 + 3; hence not 5 divides 8893 by NAT_4:9;
    8893 = 7*1270 + 3; hence not 7 divides 8893 by NAT_4:9;
    8893 = 11*808 + 5; hence not 11 divides 8893 by NAT_4:9;
    8893 = 13*684 + 1; hence not 13 divides 8893 by NAT_4:9;
    8893 = 17*523 + 2; hence not 17 divides 8893 by NAT_4:9;
    8893 = 19*468 + 1; hence not 19 divides 8893 by NAT_4:9;
    8893 = 23*386 + 15; hence not 23 divides 8893 by NAT_4:9;
    8893 = 29*306 + 19; hence not 29 divides 8893 by NAT_4:9;
    8893 = 31*286 + 27; hence not 31 divides 8893 by NAT_4:9;
    8893 = 37*240 + 13; hence not 37 divides 8893 by NAT_4:9;
    8893 = 41*216 + 37; hence not 41 divides 8893 by NAT_4:9;
    8893 = 43*206 + 35; hence not 43 divides 8893 by NAT_4:9;
    8893 = 47*189 + 10; hence not 47 divides 8893 by NAT_4:9;
    8893 = 53*167 + 42; hence not 53 divides 8893 by NAT_4:9;
    8893 = 59*150 + 43; hence not 59 divides 8893 by NAT_4:9;
    8893 = 61*145 + 48; hence not 61 divides 8893 by NAT_4:9;
    8893 = 67*132 + 49; hence not 67 divides 8893 by NAT_4:9;
    8893 = 71*125 + 18; hence not 71 divides 8893 by NAT_4:9;
    8893 = 73*121 + 60; hence not 73 divides 8893 by NAT_4:9;
    8893 = 79*112 + 45; hence not 79 divides 8893 by NAT_4:9;
    8893 = 83*107 + 12; hence not 83 divides 8893 by NAT_4:9;
    8893 = 89*99 + 82; hence not 89 divides 8893 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8893 & n is prime
  holds not n divides 8893 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
