
theorem
  9161 is prime
proof
  now
    9161 = 2*4580 + 1; hence not 2 divides 9161 by NAT_4:9;
    9161 = 3*3053 + 2; hence not 3 divides 9161 by NAT_4:9;
    9161 = 5*1832 + 1; hence not 5 divides 9161 by NAT_4:9;
    9161 = 7*1308 + 5; hence not 7 divides 9161 by NAT_4:9;
    9161 = 11*832 + 9; hence not 11 divides 9161 by NAT_4:9;
    9161 = 13*704 + 9; hence not 13 divides 9161 by NAT_4:9;
    9161 = 17*538 + 15; hence not 17 divides 9161 by NAT_4:9;
    9161 = 19*482 + 3; hence not 19 divides 9161 by NAT_4:9;
    9161 = 23*398 + 7; hence not 23 divides 9161 by NAT_4:9;
    9161 = 29*315 + 26; hence not 29 divides 9161 by NAT_4:9;
    9161 = 31*295 + 16; hence not 31 divides 9161 by NAT_4:9;
    9161 = 37*247 + 22; hence not 37 divides 9161 by NAT_4:9;
    9161 = 41*223 + 18; hence not 41 divides 9161 by NAT_4:9;
    9161 = 43*213 + 2; hence not 43 divides 9161 by NAT_4:9;
    9161 = 47*194 + 43; hence not 47 divides 9161 by NAT_4:9;
    9161 = 53*172 + 45; hence not 53 divides 9161 by NAT_4:9;
    9161 = 59*155 + 16; hence not 59 divides 9161 by NAT_4:9;
    9161 = 61*150 + 11; hence not 61 divides 9161 by NAT_4:9;
    9161 = 67*136 + 49; hence not 67 divides 9161 by NAT_4:9;
    9161 = 71*129 + 2; hence not 71 divides 9161 by NAT_4:9;
    9161 = 73*125 + 36; hence not 73 divides 9161 by NAT_4:9;
    9161 = 79*115 + 76; hence not 79 divides 9161 by NAT_4:9;
    9161 = 83*110 + 31; hence not 83 divides 9161 by NAT_4:9;
    9161 = 89*102 + 83; hence not 89 divides 9161 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9161 & n is prime
  holds not n divides 9161 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
