
theorem
  9887 is prime
proof
  now
    9887 = 2*4943 + 1; hence not 2 divides 9887 by NAT_4:9;
    9887 = 3*3295 + 2; hence not 3 divides 9887 by NAT_4:9;
    9887 = 5*1977 + 2; hence not 5 divides 9887 by NAT_4:9;
    9887 = 7*1412 + 3; hence not 7 divides 9887 by NAT_4:9;
    9887 = 11*898 + 9; hence not 11 divides 9887 by NAT_4:9;
    9887 = 13*760 + 7; hence not 13 divides 9887 by NAT_4:9;
    9887 = 17*581 + 10; hence not 17 divides 9887 by NAT_4:9;
    9887 = 19*520 + 7; hence not 19 divides 9887 by NAT_4:9;
    9887 = 23*429 + 20; hence not 23 divides 9887 by NAT_4:9;
    9887 = 29*340 + 27; hence not 29 divides 9887 by NAT_4:9;
    9887 = 31*318 + 29; hence not 31 divides 9887 by NAT_4:9;
    9887 = 37*267 + 8; hence not 37 divides 9887 by NAT_4:9;
    9887 = 41*241 + 6; hence not 41 divides 9887 by NAT_4:9;
    9887 = 43*229 + 40; hence not 43 divides 9887 by NAT_4:9;
    9887 = 47*210 + 17; hence not 47 divides 9887 by NAT_4:9;
    9887 = 53*186 + 29; hence not 53 divides 9887 by NAT_4:9;
    9887 = 59*167 + 34; hence not 59 divides 9887 by NAT_4:9;
    9887 = 61*162 + 5; hence not 61 divides 9887 by NAT_4:9;
    9887 = 67*147 + 38; hence not 67 divides 9887 by NAT_4:9;
    9887 = 71*139 + 18; hence not 71 divides 9887 by NAT_4:9;
    9887 = 73*135 + 32; hence not 73 divides 9887 by NAT_4:9;
    9887 = 79*125 + 12; hence not 79 divides 9887 by NAT_4:9;
    9887 = 83*119 + 10; hence not 83 divides 9887 by NAT_4:9;
    9887 = 89*111 + 8; hence not 89 divides 9887 by NAT_4:9;
    9887 = 97*101 + 90; hence not 97 divides 9887 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9887 & n is prime
  holds not n divides 9887 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
