
theorem
  9227 is prime
proof
  now
    9227 = 2*4613 + 1; hence not 2 divides 9227 by NAT_4:9;
    9227 = 3*3075 + 2; hence not 3 divides 9227 by NAT_4:9;
    9227 = 5*1845 + 2; hence not 5 divides 9227 by NAT_4:9;
    9227 = 7*1318 + 1; hence not 7 divides 9227 by NAT_4:9;
    9227 = 11*838 + 9; hence not 11 divides 9227 by NAT_4:9;
    9227 = 13*709 + 10; hence not 13 divides 9227 by NAT_4:9;
    9227 = 17*542 + 13; hence not 17 divides 9227 by NAT_4:9;
    9227 = 19*485 + 12; hence not 19 divides 9227 by NAT_4:9;
    9227 = 23*401 + 4; hence not 23 divides 9227 by NAT_4:9;
    9227 = 29*318 + 5; hence not 29 divides 9227 by NAT_4:9;
    9227 = 31*297 + 20; hence not 31 divides 9227 by NAT_4:9;
    9227 = 37*249 + 14; hence not 37 divides 9227 by NAT_4:9;
    9227 = 41*225 + 2; hence not 41 divides 9227 by NAT_4:9;
    9227 = 43*214 + 25; hence not 43 divides 9227 by NAT_4:9;
    9227 = 47*196 + 15; hence not 47 divides 9227 by NAT_4:9;
    9227 = 53*174 + 5; hence not 53 divides 9227 by NAT_4:9;
    9227 = 59*156 + 23; hence not 59 divides 9227 by NAT_4:9;
    9227 = 61*151 + 16; hence not 61 divides 9227 by NAT_4:9;
    9227 = 67*137 + 48; hence not 67 divides 9227 by NAT_4:9;
    9227 = 71*129 + 68; hence not 71 divides 9227 by NAT_4:9;
    9227 = 73*126 + 29; hence not 73 divides 9227 by NAT_4:9;
    9227 = 79*116 + 63; hence not 79 divides 9227 by NAT_4:9;
    9227 = 83*111 + 14; hence not 83 divides 9227 by NAT_4:9;
    9227 = 89*103 + 60; hence not 89 divides 9227 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9227 & n is prime
  holds not n divides 9227 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
