
theorem
  6551 is prime
proof
  now
    6551 = 2*3275 + 1; hence not 2 divides 6551 by NAT_4:9;
    6551 = 3*2183 + 2; hence not 3 divides 6551 by NAT_4:9;
    6551 = 5*1310 + 1; hence not 5 divides 6551 by NAT_4:9;
    6551 = 7*935 + 6; hence not 7 divides 6551 by NAT_4:9;
    6551 = 11*595 + 6; hence not 11 divides 6551 by NAT_4:9;
    6551 = 13*503 + 12; hence not 13 divides 6551 by NAT_4:9;
    6551 = 17*385 + 6; hence not 17 divides 6551 by NAT_4:9;
    6551 = 19*344 + 15; hence not 19 divides 6551 by NAT_4:9;
    6551 = 23*284 + 19; hence not 23 divides 6551 by NAT_4:9;
    6551 = 29*225 + 26; hence not 29 divides 6551 by NAT_4:9;
    6551 = 31*211 + 10; hence not 31 divides 6551 by NAT_4:9;
    6551 = 37*177 + 2; hence not 37 divides 6551 by NAT_4:9;
    6551 = 41*159 + 32; hence not 41 divides 6551 by NAT_4:9;
    6551 = 43*152 + 15; hence not 43 divides 6551 by NAT_4:9;
    6551 = 47*139 + 18; hence not 47 divides 6551 by NAT_4:9;
    6551 = 53*123 + 32; hence not 53 divides 6551 by NAT_4:9;
    6551 = 59*111 + 2; hence not 59 divides 6551 by NAT_4:9;
    6551 = 61*107 + 24; hence not 61 divides 6551 by NAT_4:9;
    6551 = 67*97 + 52; hence not 67 divides 6551 by NAT_4:9;
    6551 = 71*92 + 19; hence not 71 divides 6551 by NAT_4:9;
    6551 = 73*89 + 54; hence not 73 divides 6551 by NAT_4:9;
    6551 = 79*82 + 73; hence not 79 divides 6551 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6551 & n is prime
  holds not n divides 6551 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
