
theorem
  8887 is prime
proof
  now
    8887 = 2*4443 + 1; hence not 2 divides 8887 by NAT_4:9;
    8887 = 3*2962 + 1; hence not 3 divides 8887 by NAT_4:9;
    8887 = 5*1777 + 2; hence not 5 divides 8887 by NAT_4:9;
    8887 = 7*1269 + 4; hence not 7 divides 8887 by NAT_4:9;
    8887 = 11*807 + 10; hence not 11 divides 8887 by NAT_4:9;
    8887 = 13*683 + 8; hence not 13 divides 8887 by NAT_4:9;
    8887 = 17*522 + 13; hence not 17 divides 8887 by NAT_4:9;
    8887 = 19*467 + 14; hence not 19 divides 8887 by NAT_4:9;
    8887 = 23*386 + 9; hence not 23 divides 8887 by NAT_4:9;
    8887 = 29*306 + 13; hence not 29 divides 8887 by NAT_4:9;
    8887 = 31*286 + 21; hence not 31 divides 8887 by NAT_4:9;
    8887 = 37*240 + 7; hence not 37 divides 8887 by NAT_4:9;
    8887 = 41*216 + 31; hence not 41 divides 8887 by NAT_4:9;
    8887 = 43*206 + 29; hence not 43 divides 8887 by NAT_4:9;
    8887 = 47*189 + 4; hence not 47 divides 8887 by NAT_4:9;
    8887 = 53*167 + 36; hence not 53 divides 8887 by NAT_4:9;
    8887 = 59*150 + 37; hence not 59 divides 8887 by NAT_4:9;
    8887 = 61*145 + 42; hence not 61 divides 8887 by NAT_4:9;
    8887 = 67*132 + 43; hence not 67 divides 8887 by NAT_4:9;
    8887 = 71*125 + 12; hence not 71 divides 8887 by NAT_4:9;
    8887 = 73*121 + 54; hence not 73 divides 8887 by NAT_4:9;
    8887 = 79*112 + 39; hence not 79 divides 8887 by NAT_4:9;
    8887 = 83*107 + 6; hence not 83 divides 8887 by NAT_4:9;
    8887 = 89*99 + 76; hence not 89 divides 8887 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8887 & n is prime
  holds not n divides 8887 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
