
theorem
  7177 is prime
proof
  now
    7177 = 2*3588 + 1; hence not 2 divides 7177 by NAT_4:9;
    7177 = 3*2392 + 1; hence not 3 divides 7177 by NAT_4:9;
    7177 = 5*1435 + 2; hence not 5 divides 7177 by NAT_4:9;
    7177 = 7*1025 + 2; hence not 7 divides 7177 by NAT_4:9;
    7177 = 11*652 + 5; hence not 11 divides 7177 by NAT_4:9;
    7177 = 13*552 + 1; hence not 13 divides 7177 by NAT_4:9;
    7177 = 17*422 + 3; hence not 17 divides 7177 by NAT_4:9;
    7177 = 19*377 + 14; hence not 19 divides 7177 by NAT_4:9;
    7177 = 23*312 + 1; hence not 23 divides 7177 by NAT_4:9;
    7177 = 29*247 + 14; hence not 29 divides 7177 by NAT_4:9;
    7177 = 31*231 + 16; hence not 31 divides 7177 by NAT_4:9;
    7177 = 37*193 + 36; hence not 37 divides 7177 by NAT_4:9;
    7177 = 41*175 + 2; hence not 41 divides 7177 by NAT_4:9;
    7177 = 43*166 + 39; hence not 43 divides 7177 by NAT_4:9;
    7177 = 47*152 + 33; hence not 47 divides 7177 by NAT_4:9;
    7177 = 53*135 + 22; hence not 53 divides 7177 by NAT_4:9;
    7177 = 59*121 + 38; hence not 59 divides 7177 by NAT_4:9;
    7177 = 61*117 + 40; hence not 61 divides 7177 by NAT_4:9;
    7177 = 67*107 + 8; hence not 67 divides 7177 by NAT_4:9;
    7177 = 71*101 + 6; hence not 71 divides 7177 by NAT_4:9;
    7177 = 73*98 + 23; hence not 73 divides 7177 by NAT_4:9;
    7177 = 79*90 + 67; hence not 79 divides 7177 by NAT_4:9;
    7177 = 83*86 + 39; hence not 83 divides 7177 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7177 & n is prime
  holds not n divides 7177 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
