
theorem
  9011 is prime
proof
  now
    9011 = 2*4505 + 1; hence not 2 divides 9011 by NAT_4:9;
    9011 = 3*3003 + 2; hence not 3 divides 9011 by NAT_4:9;
    9011 = 5*1802 + 1; hence not 5 divides 9011 by NAT_4:9;
    9011 = 7*1287 + 2; hence not 7 divides 9011 by NAT_4:9;
    9011 = 11*819 + 2; hence not 11 divides 9011 by NAT_4:9;
    9011 = 13*693 + 2; hence not 13 divides 9011 by NAT_4:9;
    9011 = 17*530 + 1; hence not 17 divides 9011 by NAT_4:9;
    9011 = 19*474 + 5; hence not 19 divides 9011 by NAT_4:9;
    9011 = 23*391 + 18; hence not 23 divides 9011 by NAT_4:9;
    9011 = 29*310 + 21; hence not 29 divides 9011 by NAT_4:9;
    9011 = 31*290 + 21; hence not 31 divides 9011 by NAT_4:9;
    9011 = 37*243 + 20; hence not 37 divides 9011 by NAT_4:9;
    9011 = 41*219 + 32; hence not 41 divides 9011 by NAT_4:9;
    9011 = 43*209 + 24; hence not 43 divides 9011 by NAT_4:9;
    9011 = 47*191 + 34; hence not 47 divides 9011 by NAT_4:9;
    9011 = 53*170 + 1; hence not 53 divides 9011 by NAT_4:9;
    9011 = 59*152 + 43; hence not 59 divides 9011 by NAT_4:9;
    9011 = 61*147 + 44; hence not 61 divides 9011 by NAT_4:9;
    9011 = 67*134 + 33; hence not 67 divides 9011 by NAT_4:9;
    9011 = 71*126 + 65; hence not 71 divides 9011 by NAT_4:9;
    9011 = 73*123 + 32; hence not 73 divides 9011 by NAT_4:9;
    9011 = 79*114 + 5; hence not 79 divides 9011 by NAT_4:9;
    9011 = 83*108 + 47; hence not 83 divides 9011 by NAT_4:9;
    9011 = 89*101 + 22; hence not 89 divides 9011 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9011 & n is prime
  holds not n divides 9011 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
