
theorem
  6481 is prime
proof
  now
    6481 = 2*3240 + 1; hence not 2 divides 6481 by NAT_4:9;
    6481 = 3*2160 + 1; hence not 3 divides 6481 by NAT_4:9;
    6481 = 5*1296 + 1; hence not 5 divides 6481 by NAT_4:9;
    6481 = 7*925 + 6; hence not 7 divides 6481 by NAT_4:9;
    6481 = 11*589 + 2; hence not 11 divides 6481 by NAT_4:9;
    6481 = 13*498 + 7; hence not 13 divides 6481 by NAT_4:9;
    6481 = 17*381 + 4; hence not 17 divides 6481 by NAT_4:9;
    6481 = 19*341 + 2; hence not 19 divides 6481 by NAT_4:9;
    6481 = 23*281 + 18; hence not 23 divides 6481 by NAT_4:9;
    6481 = 29*223 + 14; hence not 29 divides 6481 by NAT_4:9;
    6481 = 31*209 + 2; hence not 31 divides 6481 by NAT_4:9;
    6481 = 37*175 + 6; hence not 37 divides 6481 by NAT_4:9;
    6481 = 41*158 + 3; hence not 41 divides 6481 by NAT_4:9;
    6481 = 43*150 + 31; hence not 43 divides 6481 by NAT_4:9;
    6481 = 47*137 + 42; hence not 47 divides 6481 by NAT_4:9;
    6481 = 53*122 + 15; hence not 53 divides 6481 by NAT_4:9;
    6481 = 59*109 + 50; hence not 59 divides 6481 by NAT_4:9;
    6481 = 61*106 + 15; hence not 61 divides 6481 by NAT_4:9;
    6481 = 67*96 + 49; hence not 67 divides 6481 by NAT_4:9;
    6481 = 71*91 + 20; hence not 71 divides 6481 by NAT_4:9;
    6481 = 73*88 + 57; hence not 73 divides 6481 by NAT_4:9;
    6481 = 79*82 + 3; hence not 79 divides 6481 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6481 & n is prime
  holds not n divides 6481 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
