
theorem
  6451 is prime
proof
  now
    6451 = 2*3225 + 1; hence not 2 divides 6451 by NAT_4:9;
    6451 = 3*2150 + 1; hence not 3 divides 6451 by NAT_4:9;
    6451 = 5*1290 + 1; hence not 5 divides 6451 by NAT_4:9;
    6451 = 7*921 + 4; hence not 7 divides 6451 by NAT_4:9;
    6451 = 11*586 + 5; hence not 11 divides 6451 by NAT_4:9;
    6451 = 13*496 + 3; hence not 13 divides 6451 by NAT_4:9;
    6451 = 17*379 + 8; hence not 17 divides 6451 by NAT_4:9;
    6451 = 19*339 + 10; hence not 19 divides 6451 by NAT_4:9;
    6451 = 23*280 + 11; hence not 23 divides 6451 by NAT_4:9;
    6451 = 29*222 + 13; hence not 29 divides 6451 by NAT_4:9;
    6451 = 31*208 + 3; hence not 31 divides 6451 by NAT_4:9;
    6451 = 37*174 + 13; hence not 37 divides 6451 by NAT_4:9;
    6451 = 41*157 + 14; hence not 41 divides 6451 by NAT_4:9;
    6451 = 43*150 + 1; hence not 43 divides 6451 by NAT_4:9;
    6451 = 47*137 + 12; hence not 47 divides 6451 by NAT_4:9;
    6451 = 53*121 + 38; hence not 53 divides 6451 by NAT_4:9;
    6451 = 59*109 + 20; hence not 59 divides 6451 by NAT_4:9;
    6451 = 61*105 + 46; hence not 61 divides 6451 by NAT_4:9;
    6451 = 67*96 + 19; hence not 67 divides 6451 by NAT_4:9;
    6451 = 71*90 + 61; hence not 71 divides 6451 by NAT_4:9;
    6451 = 73*88 + 27; hence not 73 divides 6451 by NAT_4:9;
    6451 = 79*81 + 52; hence not 79 divides 6451 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6451 & n is prime
  holds not n divides 6451 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
