
theorem
  6521 is prime
proof
  now
    6521 = 2*3260 + 1; hence not 2 divides 6521 by NAT_4:9;
    6521 = 3*2173 + 2; hence not 3 divides 6521 by NAT_4:9;
    6521 = 5*1304 + 1; hence not 5 divides 6521 by NAT_4:9;
    6521 = 7*931 + 4; hence not 7 divides 6521 by NAT_4:9;
    6521 = 11*592 + 9; hence not 11 divides 6521 by NAT_4:9;
    6521 = 13*501 + 8; hence not 13 divides 6521 by NAT_4:9;
    6521 = 17*383 + 10; hence not 17 divides 6521 by NAT_4:9;
    6521 = 19*343 + 4; hence not 19 divides 6521 by NAT_4:9;
    6521 = 23*283 + 12; hence not 23 divides 6521 by NAT_4:9;
    6521 = 29*224 + 25; hence not 29 divides 6521 by NAT_4:9;
    6521 = 31*210 + 11; hence not 31 divides 6521 by NAT_4:9;
    6521 = 37*176 + 9; hence not 37 divides 6521 by NAT_4:9;
    6521 = 41*159 + 2; hence not 41 divides 6521 by NAT_4:9;
    6521 = 43*151 + 28; hence not 43 divides 6521 by NAT_4:9;
    6521 = 47*138 + 35; hence not 47 divides 6521 by NAT_4:9;
    6521 = 53*123 + 2; hence not 53 divides 6521 by NAT_4:9;
    6521 = 59*110 + 31; hence not 59 divides 6521 by NAT_4:9;
    6521 = 61*106 + 55; hence not 61 divides 6521 by NAT_4:9;
    6521 = 67*97 + 22; hence not 67 divides 6521 by NAT_4:9;
    6521 = 71*91 + 60; hence not 71 divides 6521 by NAT_4:9;
    6521 = 73*89 + 24; hence not 73 divides 6521 by NAT_4:9;
    6521 = 79*82 + 43; hence not 79 divides 6521 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6521 & n is prime
  holds not n divides 6521 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
