
theorem
  9209 is prime
proof
  now
    9209 = 2*4604 + 1; hence not 2 divides 9209 by NAT_4:9;
    9209 = 3*3069 + 2; hence not 3 divides 9209 by NAT_4:9;
    9209 = 5*1841 + 4; hence not 5 divides 9209 by NAT_4:9;
    9209 = 7*1315 + 4; hence not 7 divides 9209 by NAT_4:9;
    9209 = 11*837 + 2; hence not 11 divides 9209 by NAT_4:9;
    9209 = 13*708 + 5; hence not 13 divides 9209 by NAT_4:9;
    9209 = 17*541 + 12; hence not 17 divides 9209 by NAT_4:9;
    9209 = 19*484 + 13; hence not 19 divides 9209 by NAT_4:9;
    9209 = 23*400 + 9; hence not 23 divides 9209 by NAT_4:9;
    9209 = 29*317 + 16; hence not 29 divides 9209 by NAT_4:9;
    9209 = 31*297 + 2; hence not 31 divides 9209 by NAT_4:9;
    9209 = 37*248 + 33; hence not 37 divides 9209 by NAT_4:9;
    9209 = 41*224 + 25; hence not 41 divides 9209 by NAT_4:9;
    9209 = 43*214 + 7; hence not 43 divides 9209 by NAT_4:9;
    9209 = 47*195 + 44; hence not 47 divides 9209 by NAT_4:9;
    9209 = 53*173 + 40; hence not 53 divides 9209 by NAT_4:9;
    9209 = 59*156 + 5; hence not 59 divides 9209 by NAT_4:9;
    9209 = 61*150 + 59; hence not 61 divides 9209 by NAT_4:9;
    9209 = 67*137 + 30; hence not 67 divides 9209 by NAT_4:9;
    9209 = 71*129 + 50; hence not 71 divides 9209 by NAT_4:9;
    9209 = 73*126 + 11; hence not 73 divides 9209 by NAT_4:9;
    9209 = 79*116 + 45; hence not 79 divides 9209 by NAT_4:9;
    9209 = 83*110 + 79; hence not 83 divides 9209 by NAT_4:9;
    9209 = 89*103 + 42; hence not 89 divides 9209 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9209 & n is prime
  holds not n divides 9209 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
