
theorem
  4357 is prime
proof
  now
    4357 = 2*2178 + 1; hence not 2 divides 4357 by NAT_4:9;
    4357 = 3*1452 + 1; hence not 3 divides 4357 by NAT_4:9;
    4357 = 5*871 + 2; hence not 5 divides 4357 by NAT_4:9;
    4357 = 7*622 + 3; hence not 7 divides 4357 by NAT_4:9;
    4357 = 11*396 + 1; hence not 11 divides 4357 by NAT_4:9;
    4357 = 13*335 + 2; hence not 13 divides 4357 by NAT_4:9;
    4357 = 17*256 + 5; hence not 17 divides 4357 by NAT_4:9;
    4357 = 19*229 + 6; hence not 19 divides 4357 by NAT_4:9;
    4357 = 23*189 + 10; hence not 23 divides 4357 by NAT_4:9;
    4357 = 29*150 + 7; hence not 29 divides 4357 by NAT_4:9;
    4357 = 31*140 + 17; hence not 31 divides 4357 by NAT_4:9;
    4357 = 37*117 + 28; hence not 37 divides 4357 by NAT_4:9;
    4357 = 41*106 + 11; hence not 41 divides 4357 by NAT_4:9;
    4357 = 43*101 + 14; hence not 43 divides 4357 by NAT_4:9;
    4357 = 47*92 + 33; hence not 47 divides 4357 by NAT_4:9;
    4357 = 53*82 + 11; hence not 53 divides 4357 by NAT_4:9;
    4357 = 59*73 + 50; hence not 59 divides 4357 by NAT_4:9;
    4357 = 61*71 + 26; hence not 61 divides 4357 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4357 & n is prime
  holds not n divides 4357 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
