
theorem
  9181 is prime
proof
  now
    9181 = 2*4590 + 1; hence not 2 divides 9181 by NAT_4:9;
    9181 = 3*3060 + 1; hence not 3 divides 9181 by NAT_4:9;
    9181 = 5*1836 + 1; hence not 5 divides 9181 by NAT_4:9;
    9181 = 7*1311 + 4; hence not 7 divides 9181 by NAT_4:9;
    9181 = 11*834 + 7; hence not 11 divides 9181 by NAT_4:9;
    9181 = 13*706 + 3; hence not 13 divides 9181 by NAT_4:9;
    9181 = 17*540 + 1; hence not 17 divides 9181 by NAT_4:9;
    9181 = 19*483 + 4; hence not 19 divides 9181 by NAT_4:9;
    9181 = 23*399 + 4; hence not 23 divides 9181 by NAT_4:9;
    9181 = 29*316 + 17; hence not 29 divides 9181 by NAT_4:9;
    9181 = 31*296 + 5; hence not 31 divides 9181 by NAT_4:9;
    9181 = 37*248 + 5; hence not 37 divides 9181 by NAT_4:9;
    9181 = 41*223 + 38; hence not 41 divides 9181 by NAT_4:9;
    9181 = 43*213 + 22; hence not 43 divides 9181 by NAT_4:9;
    9181 = 47*195 + 16; hence not 47 divides 9181 by NAT_4:9;
    9181 = 53*173 + 12; hence not 53 divides 9181 by NAT_4:9;
    9181 = 59*155 + 36; hence not 59 divides 9181 by NAT_4:9;
    9181 = 61*150 + 31; hence not 61 divides 9181 by NAT_4:9;
    9181 = 67*137 + 2; hence not 67 divides 9181 by NAT_4:9;
    9181 = 71*129 + 22; hence not 71 divides 9181 by NAT_4:9;
    9181 = 73*125 + 56; hence not 73 divides 9181 by NAT_4:9;
    9181 = 79*116 + 17; hence not 79 divides 9181 by NAT_4:9;
    9181 = 83*110 + 51; hence not 83 divides 9181 by NAT_4:9;
    9181 = 89*103 + 14; hence not 89 divides 9181 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9181 & n is prime
  holds not n divides 9181 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
