
theorem
  4423 is prime
proof
  now
    4423 = 2*2211 + 1; hence not 2 divides 4423 by NAT_4:9;
    4423 = 3*1474 + 1; hence not 3 divides 4423 by NAT_4:9;
    4423 = 5*884 + 3; hence not 5 divides 4423 by NAT_4:9;
    4423 = 7*631 + 6; hence not 7 divides 4423 by NAT_4:9;
    4423 = 11*402 + 1; hence not 11 divides 4423 by NAT_4:9;
    4423 = 13*340 + 3; hence not 13 divides 4423 by NAT_4:9;
    4423 = 17*260 + 3; hence not 17 divides 4423 by NAT_4:9;
    4423 = 19*232 + 15; hence not 19 divides 4423 by NAT_4:9;
    4423 = 23*192 + 7; hence not 23 divides 4423 by NAT_4:9;
    4423 = 29*152 + 15; hence not 29 divides 4423 by NAT_4:9;
    4423 = 31*142 + 21; hence not 31 divides 4423 by NAT_4:9;
    4423 = 37*119 + 20; hence not 37 divides 4423 by NAT_4:9;
    4423 = 41*107 + 36; hence not 41 divides 4423 by NAT_4:9;
    4423 = 43*102 + 37; hence not 43 divides 4423 by NAT_4:9;
    4423 = 47*94 + 5; hence not 47 divides 4423 by NAT_4:9;
    4423 = 53*83 + 24; hence not 53 divides 4423 by NAT_4:9;
    4423 = 59*74 + 57; hence not 59 divides 4423 by NAT_4:9;
    4423 = 61*72 + 31; hence not 61 divides 4423 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4423 & n is prime
  holds not n divides 4423 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
