
theorem
  4327 is prime
proof
  now
    4327 = 2*2163 + 1; hence not 2 divides 4327 by NAT_4:9;
    4327 = 3*1442 + 1; hence not 3 divides 4327 by NAT_4:9;
    4327 = 5*865 + 2; hence not 5 divides 4327 by NAT_4:9;
    4327 = 7*618 + 1; hence not 7 divides 4327 by NAT_4:9;
    4327 = 11*393 + 4; hence not 11 divides 4327 by NAT_4:9;
    4327 = 13*332 + 11; hence not 13 divides 4327 by NAT_4:9;
    4327 = 17*254 + 9; hence not 17 divides 4327 by NAT_4:9;
    4327 = 19*227 + 14; hence not 19 divides 4327 by NAT_4:9;
    4327 = 23*188 + 3; hence not 23 divides 4327 by NAT_4:9;
    4327 = 29*149 + 6; hence not 29 divides 4327 by NAT_4:9;
    4327 = 31*139 + 18; hence not 31 divides 4327 by NAT_4:9;
    4327 = 37*116 + 35; hence not 37 divides 4327 by NAT_4:9;
    4327 = 41*105 + 22; hence not 41 divides 4327 by NAT_4:9;
    4327 = 43*100 + 27; hence not 43 divides 4327 by NAT_4:9;
    4327 = 47*92 + 3; hence not 47 divides 4327 by NAT_4:9;
    4327 = 53*81 + 34; hence not 53 divides 4327 by NAT_4:9;
    4327 = 59*73 + 20; hence not 59 divides 4327 by NAT_4:9;
    4327 = 61*70 + 57; hence not 61 divides 4327 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4327 & n is prime
  holds not n divides 4327 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
