
theorem
  8963 is prime
proof
  now
    8963 = 2*4481 + 1; hence not 2 divides 8963 by NAT_4:9;
    8963 = 3*2987 + 2; hence not 3 divides 8963 by NAT_4:9;
    8963 = 5*1792 + 3; hence not 5 divides 8963 by NAT_4:9;
    8963 = 7*1280 + 3; hence not 7 divides 8963 by NAT_4:9;
    8963 = 11*814 + 9; hence not 11 divides 8963 by NAT_4:9;
    8963 = 13*689 + 6; hence not 13 divides 8963 by NAT_4:9;
    8963 = 17*527 + 4; hence not 17 divides 8963 by NAT_4:9;
    8963 = 19*471 + 14; hence not 19 divides 8963 by NAT_4:9;
    8963 = 23*389 + 16; hence not 23 divides 8963 by NAT_4:9;
    8963 = 29*309 + 2; hence not 29 divides 8963 by NAT_4:9;
    8963 = 31*289 + 4; hence not 31 divides 8963 by NAT_4:9;
    8963 = 37*242 + 9; hence not 37 divides 8963 by NAT_4:9;
    8963 = 41*218 + 25; hence not 41 divides 8963 by NAT_4:9;
    8963 = 43*208 + 19; hence not 43 divides 8963 by NAT_4:9;
    8963 = 47*190 + 33; hence not 47 divides 8963 by NAT_4:9;
    8963 = 53*169 + 6; hence not 53 divides 8963 by NAT_4:9;
    8963 = 59*151 + 54; hence not 59 divides 8963 by NAT_4:9;
    8963 = 61*146 + 57; hence not 61 divides 8963 by NAT_4:9;
    8963 = 67*133 + 52; hence not 67 divides 8963 by NAT_4:9;
    8963 = 71*126 + 17; hence not 71 divides 8963 by NAT_4:9;
    8963 = 73*122 + 57; hence not 73 divides 8963 by NAT_4:9;
    8963 = 79*113 + 36; hence not 79 divides 8963 by NAT_4:9;
    8963 = 83*107 + 82; hence not 83 divides 8963 by NAT_4:9;
    8963 = 89*100 + 63; hence not 89 divides 8963 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8963 & n is prime
  holds not n divides 8963 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
