
theorem
  4229 is prime
proof
  now
    4229 = 2*2114 + 1; hence not 2 divides 4229 by NAT_4:9;
    4229 = 3*1409 + 2; hence not 3 divides 4229 by NAT_4:9;
    4229 = 5*845 + 4; hence not 5 divides 4229 by NAT_4:9;
    4229 = 7*604 + 1; hence not 7 divides 4229 by NAT_4:9;
    4229 = 11*384 + 5; hence not 11 divides 4229 by NAT_4:9;
    4229 = 13*325 + 4; hence not 13 divides 4229 by NAT_4:9;
    4229 = 17*248 + 13; hence not 17 divides 4229 by NAT_4:9;
    4229 = 19*222 + 11; hence not 19 divides 4229 by NAT_4:9;
    4229 = 23*183 + 20; hence not 23 divides 4229 by NAT_4:9;
    4229 = 29*145 + 24; hence not 29 divides 4229 by NAT_4:9;
    4229 = 31*136 + 13; hence not 31 divides 4229 by NAT_4:9;
    4229 = 37*114 + 11; hence not 37 divides 4229 by NAT_4:9;
    4229 = 41*103 + 6; hence not 41 divides 4229 by NAT_4:9;
    4229 = 43*98 + 15; hence not 43 divides 4229 by NAT_4:9;
    4229 = 47*89 + 46; hence not 47 divides 4229 by NAT_4:9;
    4229 = 53*79 + 42; hence not 53 divides 4229 by NAT_4:9;
    4229 = 59*71 + 40; hence not 59 divides 4229 by NAT_4:9;
    4229 = 61*69 + 20; hence not 61 divides 4229 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4229 & n is prime
  holds not n divides 4229 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
