
theorem
  2423 is prime
proof
  now
    2423 = 2*1211 + 1; hence not 2 divides 2423 by NAT_4:9;
    2423 = 3*807 + 2; hence not 3 divides 2423 by NAT_4:9;
    2423 = 5*484 + 3; hence not 5 divides 2423 by NAT_4:9;
    2423 = 7*346 + 1; hence not 7 divides 2423 by NAT_4:9;
    2423 = 11*220 + 3; hence not 11 divides 2423 by NAT_4:9;
    2423 = 13*186 + 5; hence not 13 divides 2423 by NAT_4:9;
    2423 = 17*142 + 9; hence not 17 divides 2423 by NAT_4:9;
    2423 = 19*127 + 10; hence not 19 divides 2423 by NAT_4:9;
    2423 = 23*105 + 8; hence not 23 divides 2423 by NAT_4:9;
    2423 = 29*83 + 16; hence not 29 divides 2423 by NAT_4:9;
    2423 = 31*78 + 5; hence not 31 divides 2423 by NAT_4:9;
    2423 = 37*65 + 18; hence not 37 divides 2423 by NAT_4:9;
    2423 = 41*59 + 4; hence not 41 divides 2423 by NAT_4:9;
    2423 = 43*56 + 15; hence not 43 divides 2423 by NAT_4:9;
    2423 = 47*51 + 26; hence not 47 divides 2423 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2423 & n is prime
  holds not n divides 2423 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
