
theorem
  9109 is prime
proof
  now
    9109 = 2*4554 + 1; hence not 2 divides 9109 by NAT_4:9;
    9109 = 3*3036 + 1; hence not 3 divides 9109 by NAT_4:9;
    9109 = 5*1821 + 4; hence not 5 divides 9109 by NAT_4:9;
    9109 = 7*1301 + 2; hence not 7 divides 9109 by NAT_4:9;
    9109 = 11*828 + 1; hence not 11 divides 9109 by NAT_4:9;
    9109 = 13*700 + 9; hence not 13 divides 9109 by NAT_4:9;
    9109 = 17*535 + 14; hence not 17 divides 9109 by NAT_4:9;
    9109 = 19*479 + 8; hence not 19 divides 9109 by NAT_4:9;
    9109 = 23*396 + 1; hence not 23 divides 9109 by NAT_4:9;
    9109 = 29*314 + 3; hence not 29 divides 9109 by NAT_4:9;
    9109 = 31*293 + 26; hence not 31 divides 9109 by NAT_4:9;
    9109 = 37*246 + 7; hence not 37 divides 9109 by NAT_4:9;
    9109 = 41*222 + 7; hence not 41 divides 9109 by NAT_4:9;
    9109 = 43*211 + 36; hence not 43 divides 9109 by NAT_4:9;
    9109 = 47*193 + 38; hence not 47 divides 9109 by NAT_4:9;
    9109 = 53*171 + 46; hence not 53 divides 9109 by NAT_4:9;
    9109 = 59*154 + 23; hence not 59 divides 9109 by NAT_4:9;
    9109 = 61*149 + 20; hence not 61 divides 9109 by NAT_4:9;
    9109 = 67*135 + 64; hence not 67 divides 9109 by NAT_4:9;
    9109 = 71*128 + 21; hence not 71 divides 9109 by NAT_4:9;
    9109 = 73*124 + 57; hence not 73 divides 9109 by NAT_4:9;
    9109 = 79*115 + 24; hence not 79 divides 9109 by NAT_4:9;
    9109 = 83*109 + 62; hence not 83 divides 9109 by NAT_4:9;
    9109 = 89*102 + 31; hence not 89 divides 9109 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9109 & n is prime
  holds not n divides 9109 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
