
theorem
  9199 is prime
proof
  now
    9199 = 2*4599 + 1; hence not 2 divides 9199 by NAT_4:9;
    9199 = 3*3066 + 1; hence not 3 divides 9199 by NAT_4:9;
    9199 = 5*1839 + 4; hence not 5 divides 9199 by NAT_4:9;
    9199 = 7*1314 + 1; hence not 7 divides 9199 by NAT_4:9;
    9199 = 11*836 + 3; hence not 11 divides 9199 by NAT_4:9;
    9199 = 13*707 + 8; hence not 13 divides 9199 by NAT_4:9;
    9199 = 17*541 + 2; hence not 17 divides 9199 by NAT_4:9;
    9199 = 19*484 + 3; hence not 19 divides 9199 by NAT_4:9;
    9199 = 23*399 + 22; hence not 23 divides 9199 by NAT_4:9;
    9199 = 29*317 + 6; hence not 29 divides 9199 by NAT_4:9;
    9199 = 31*296 + 23; hence not 31 divides 9199 by NAT_4:9;
    9199 = 37*248 + 23; hence not 37 divides 9199 by NAT_4:9;
    9199 = 41*224 + 15; hence not 41 divides 9199 by NAT_4:9;
    9199 = 43*213 + 40; hence not 43 divides 9199 by NAT_4:9;
    9199 = 47*195 + 34; hence not 47 divides 9199 by NAT_4:9;
    9199 = 53*173 + 30; hence not 53 divides 9199 by NAT_4:9;
    9199 = 59*155 + 54; hence not 59 divides 9199 by NAT_4:9;
    9199 = 61*150 + 49; hence not 61 divides 9199 by NAT_4:9;
    9199 = 67*137 + 20; hence not 67 divides 9199 by NAT_4:9;
    9199 = 71*129 + 40; hence not 71 divides 9199 by NAT_4:9;
    9199 = 73*126 + 1; hence not 73 divides 9199 by NAT_4:9;
    9199 = 79*116 + 35; hence not 79 divides 9199 by NAT_4:9;
    9199 = 83*110 + 69; hence not 83 divides 9199 by NAT_4:9;
    9199 = 89*103 + 32; hence not 89 divides 9199 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9199 & n is prime
  holds not n divides 9199 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
