
theorem
  6229 is prime
proof
  now
    6229 = 2*3114 + 1; hence not 2 divides 6229 by NAT_4:9;
    6229 = 3*2076 + 1; hence not 3 divides 6229 by NAT_4:9;
    6229 = 5*1245 + 4; hence not 5 divides 6229 by NAT_4:9;
    6229 = 7*889 + 6; hence not 7 divides 6229 by NAT_4:9;
    6229 = 11*566 + 3; hence not 11 divides 6229 by NAT_4:9;
    6229 = 13*479 + 2; hence not 13 divides 6229 by NAT_4:9;
    6229 = 17*366 + 7; hence not 17 divides 6229 by NAT_4:9;
    6229 = 19*327 + 16; hence not 19 divides 6229 by NAT_4:9;
    6229 = 23*270 + 19; hence not 23 divides 6229 by NAT_4:9;
    6229 = 29*214 + 23; hence not 29 divides 6229 by NAT_4:9;
    6229 = 31*200 + 29; hence not 31 divides 6229 by NAT_4:9;
    6229 = 37*168 + 13; hence not 37 divides 6229 by NAT_4:9;
    6229 = 41*151 + 38; hence not 41 divides 6229 by NAT_4:9;
    6229 = 43*144 + 37; hence not 43 divides 6229 by NAT_4:9;
    6229 = 47*132 + 25; hence not 47 divides 6229 by NAT_4:9;
    6229 = 53*117 + 28; hence not 53 divides 6229 by NAT_4:9;
    6229 = 59*105 + 34; hence not 59 divides 6229 by NAT_4:9;
    6229 = 61*102 + 7; hence not 61 divides 6229 by NAT_4:9;
    6229 = 67*92 + 65; hence not 67 divides 6229 by NAT_4:9;
    6229 = 71*87 + 52; hence not 71 divides 6229 by NAT_4:9;
    6229 = 73*85 + 24; hence not 73 divides 6229 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6229 & n is prime
  holds not n divides 6229 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
