
theorem
  6427 is prime
proof
  now
    6427 = 2*3213 + 1; hence not 2 divides 6427 by NAT_4:9;
    6427 = 3*2142 + 1; hence not 3 divides 6427 by NAT_4:9;
    6427 = 5*1285 + 2; hence not 5 divides 6427 by NAT_4:9;
    6427 = 7*918 + 1; hence not 7 divides 6427 by NAT_4:9;
    6427 = 11*584 + 3; hence not 11 divides 6427 by NAT_4:9;
    6427 = 13*494 + 5; hence not 13 divides 6427 by NAT_4:9;
    6427 = 17*378 + 1; hence not 17 divides 6427 by NAT_4:9;
    6427 = 19*338 + 5; hence not 19 divides 6427 by NAT_4:9;
    6427 = 23*279 + 10; hence not 23 divides 6427 by NAT_4:9;
    6427 = 29*221 + 18; hence not 29 divides 6427 by NAT_4:9;
    6427 = 31*207 + 10; hence not 31 divides 6427 by NAT_4:9;
    6427 = 37*173 + 26; hence not 37 divides 6427 by NAT_4:9;
    6427 = 41*156 + 31; hence not 41 divides 6427 by NAT_4:9;
    6427 = 43*149 + 20; hence not 43 divides 6427 by NAT_4:9;
    6427 = 47*136 + 35; hence not 47 divides 6427 by NAT_4:9;
    6427 = 53*121 + 14; hence not 53 divides 6427 by NAT_4:9;
    6427 = 59*108 + 55; hence not 59 divides 6427 by NAT_4:9;
    6427 = 61*105 + 22; hence not 61 divides 6427 by NAT_4:9;
    6427 = 67*95 + 62; hence not 67 divides 6427 by NAT_4:9;
    6427 = 71*90 + 37; hence not 71 divides 6427 by NAT_4:9;
    6427 = 73*88 + 3; hence not 73 divides 6427 by NAT_4:9;
    6427 = 79*81 + 28; hence not 79 divides 6427 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6427 & n is prime
  holds not n divides 6427 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
