
theorem
  9257 is prime
proof
  now
    9257 = 2*4628 + 1; hence not 2 divides 9257 by NAT_4:9;
    9257 = 3*3085 + 2; hence not 3 divides 9257 by NAT_4:9;
    9257 = 5*1851 + 2; hence not 5 divides 9257 by NAT_4:9;
    9257 = 7*1322 + 3; hence not 7 divides 9257 by NAT_4:9;
    9257 = 11*841 + 6; hence not 11 divides 9257 by NAT_4:9;
    9257 = 13*712 + 1; hence not 13 divides 9257 by NAT_4:9;
    9257 = 17*544 + 9; hence not 17 divides 9257 by NAT_4:9;
    9257 = 19*487 + 4; hence not 19 divides 9257 by NAT_4:9;
    9257 = 23*402 + 11; hence not 23 divides 9257 by NAT_4:9;
    9257 = 29*319 + 6; hence not 29 divides 9257 by NAT_4:9;
    9257 = 31*298 + 19; hence not 31 divides 9257 by NAT_4:9;
    9257 = 37*250 + 7; hence not 37 divides 9257 by NAT_4:9;
    9257 = 41*225 + 32; hence not 41 divides 9257 by NAT_4:9;
    9257 = 43*215 + 12; hence not 43 divides 9257 by NAT_4:9;
    9257 = 47*196 + 45; hence not 47 divides 9257 by NAT_4:9;
    9257 = 53*174 + 35; hence not 53 divides 9257 by NAT_4:9;
    9257 = 59*156 + 53; hence not 59 divides 9257 by NAT_4:9;
    9257 = 61*151 + 46; hence not 61 divides 9257 by NAT_4:9;
    9257 = 67*138 + 11; hence not 67 divides 9257 by NAT_4:9;
    9257 = 71*130 + 27; hence not 71 divides 9257 by NAT_4:9;
    9257 = 73*126 + 59; hence not 73 divides 9257 by NAT_4:9;
    9257 = 79*117 + 14; hence not 79 divides 9257 by NAT_4:9;
    9257 = 83*111 + 44; hence not 83 divides 9257 by NAT_4:9;
    9257 = 89*104 + 1; hence not 89 divides 9257 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9257 & n is prime
  holds not n divides 9257 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
