
theorem
  6173 is prime
proof
  now
    6173 = 2*3086 + 1; hence not 2 divides 6173 by NAT_4:9;
    6173 = 3*2057 + 2; hence not 3 divides 6173 by NAT_4:9;
    6173 = 5*1234 + 3; hence not 5 divides 6173 by NAT_4:9;
    6173 = 7*881 + 6; hence not 7 divides 6173 by NAT_4:9;
    6173 = 11*561 + 2; hence not 11 divides 6173 by NAT_4:9;
    6173 = 13*474 + 11; hence not 13 divides 6173 by NAT_4:9;
    6173 = 17*363 + 2; hence not 17 divides 6173 by NAT_4:9;
    6173 = 19*324 + 17; hence not 19 divides 6173 by NAT_4:9;
    6173 = 23*268 + 9; hence not 23 divides 6173 by NAT_4:9;
    6173 = 29*212 + 25; hence not 29 divides 6173 by NAT_4:9;
    6173 = 31*199 + 4; hence not 31 divides 6173 by NAT_4:9;
    6173 = 37*166 + 31; hence not 37 divides 6173 by NAT_4:9;
    6173 = 41*150 + 23; hence not 41 divides 6173 by NAT_4:9;
    6173 = 43*143 + 24; hence not 43 divides 6173 by NAT_4:9;
    6173 = 47*131 + 16; hence not 47 divides 6173 by NAT_4:9;
    6173 = 53*116 + 25; hence not 53 divides 6173 by NAT_4:9;
    6173 = 59*104 + 37; hence not 59 divides 6173 by NAT_4:9;
    6173 = 61*101 + 12; hence not 61 divides 6173 by NAT_4:9;
    6173 = 67*92 + 9; hence not 67 divides 6173 by NAT_4:9;
    6173 = 71*86 + 67; hence not 71 divides 6173 by NAT_4:9;
    6173 = 73*84 + 41; hence not 73 divides 6173 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6173 & n is prime
  holds not n divides 6173 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
