
theorem
  4363 is prime
proof
  now
    4363 = 2*2181 + 1; hence not 2 divides 4363 by NAT_4:9;
    4363 = 3*1454 + 1; hence not 3 divides 4363 by NAT_4:9;
    4363 = 5*872 + 3; hence not 5 divides 4363 by NAT_4:9;
    4363 = 7*623 + 2; hence not 7 divides 4363 by NAT_4:9;
    4363 = 11*396 + 7; hence not 11 divides 4363 by NAT_4:9;
    4363 = 13*335 + 8; hence not 13 divides 4363 by NAT_4:9;
    4363 = 17*256 + 11; hence not 17 divides 4363 by NAT_4:9;
    4363 = 19*229 + 12; hence not 19 divides 4363 by NAT_4:9;
    4363 = 23*189 + 16; hence not 23 divides 4363 by NAT_4:9;
    4363 = 29*150 + 13; hence not 29 divides 4363 by NAT_4:9;
    4363 = 31*140 + 23; hence not 31 divides 4363 by NAT_4:9;
    4363 = 37*117 + 34; hence not 37 divides 4363 by NAT_4:9;
    4363 = 41*106 + 17; hence not 41 divides 4363 by NAT_4:9;
    4363 = 43*101 + 20; hence not 43 divides 4363 by NAT_4:9;
    4363 = 47*92 + 39; hence not 47 divides 4363 by NAT_4:9;
    4363 = 53*82 + 17; hence not 53 divides 4363 by NAT_4:9;
    4363 = 59*73 + 56; hence not 59 divides 4363 by NAT_4:9;
    4363 = 61*71 + 32; hence not 61 divides 4363 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4363 & n is prime
  holds not n divides 4363 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
