
theorem
  6553 is prime
proof
  now
    6553 = 2*3276 + 1; hence not 2 divides 6553 by NAT_4:9;
    6553 = 3*2184 + 1; hence not 3 divides 6553 by NAT_4:9;
    6553 = 5*1310 + 3; hence not 5 divides 6553 by NAT_4:9;
    6553 = 7*936 + 1; hence not 7 divides 6553 by NAT_4:9;
    6553 = 11*595 + 8; hence not 11 divides 6553 by NAT_4:9;
    6553 = 13*504 + 1; hence not 13 divides 6553 by NAT_4:9;
    6553 = 17*385 + 8; hence not 17 divides 6553 by NAT_4:9;
    6553 = 19*344 + 17; hence not 19 divides 6553 by NAT_4:9;
    6553 = 23*284 + 21; hence not 23 divides 6553 by NAT_4:9;
    6553 = 29*225 + 28; hence not 29 divides 6553 by NAT_4:9;
    6553 = 31*211 + 12; hence not 31 divides 6553 by NAT_4:9;
    6553 = 37*177 + 4; hence not 37 divides 6553 by NAT_4:9;
    6553 = 41*159 + 34; hence not 41 divides 6553 by NAT_4:9;
    6553 = 43*152 + 17; hence not 43 divides 6553 by NAT_4:9;
    6553 = 47*139 + 20; hence not 47 divides 6553 by NAT_4:9;
    6553 = 53*123 + 34; hence not 53 divides 6553 by NAT_4:9;
    6553 = 59*111 + 4; hence not 59 divides 6553 by NAT_4:9;
    6553 = 61*107 + 26; hence not 61 divides 6553 by NAT_4:9;
    6553 = 67*97 + 54; hence not 67 divides 6553 by NAT_4:9;
    6553 = 71*92 + 21; hence not 71 divides 6553 by NAT_4:9;
    6553 = 73*89 + 56; hence not 73 divides 6553 by NAT_4:9;
    6553 = 79*82 + 75; hence not 79 divides 6553 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6553 & n is prime
  holds not n divides 6553 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
