
theorem
  6529 is prime
proof
  now
    6529 = 2*3264 + 1; hence not 2 divides 6529 by NAT_4:9;
    6529 = 3*2176 + 1; hence not 3 divides 6529 by NAT_4:9;
    6529 = 5*1305 + 4; hence not 5 divides 6529 by NAT_4:9;
    6529 = 7*932 + 5; hence not 7 divides 6529 by NAT_4:9;
    6529 = 11*593 + 6; hence not 11 divides 6529 by NAT_4:9;
    6529 = 13*502 + 3; hence not 13 divides 6529 by NAT_4:9;
    6529 = 17*384 + 1; hence not 17 divides 6529 by NAT_4:9;
    6529 = 19*343 + 12; hence not 19 divides 6529 by NAT_4:9;
    6529 = 23*283 + 20; hence not 23 divides 6529 by NAT_4:9;
    6529 = 29*225 + 4; hence not 29 divides 6529 by NAT_4:9;
    6529 = 31*210 + 19; hence not 31 divides 6529 by NAT_4:9;
    6529 = 37*176 + 17; hence not 37 divides 6529 by NAT_4:9;
    6529 = 41*159 + 10; hence not 41 divides 6529 by NAT_4:9;
    6529 = 43*151 + 36; hence not 43 divides 6529 by NAT_4:9;
    6529 = 47*138 + 43; hence not 47 divides 6529 by NAT_4:9;
    6529 = 53*123 + 10; hence not 53 divides 6529 by NAT_4:9;
    6529 = 59*110 + 39; hence not 59 divides 6529 by NAT_4:9;
    6529 = 61*107 + 2; hence not 61 divides 6529 by NAT_4:9;
    6529 = 67*97 + 30; hence not 67 divides 6529 by NAT_4:9;
    6529 = 71*91 + 68; hence not 71 divides 6529 by NAT_4:9;
    6529 = 73*89 + 32; hence not 73 divides 6529 by NAT_4:9;
    6529 = 79*82 + 51; hence not 79 divides 6529 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6529 & n is prime
  holds not n divides 6529 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
