
theorem
  1423 is prime
proof
  now
    1423 = 2*711 + 1; hence not 2 divides 1423 by NAT_4:9;
    1423 = 3*474 + 1; hence not 3 divides 1423 by NAT_4:9;
    1423 = 5*284 + 3; hence not 5 divides 1423 by NAT_4:9;
    1423 = 7*203 + 2; hence not 7 divides 1423 by NAT_4:9;
    1423 = 11*129 + 4; hence not 11 divides 1423 by NAT_4:9;
    1423 = 13*109 + 6; hence not 13 divides 1423 by NAT_4:9;
    1423 = 17*83 + 12; hence not 17 divides 1423 by NAT_4:9;
    1423 = 19*74 + 17; hence not 19 divides 1423 by NAT_4:9;
    1423 = 23*61 + 20; hence not 23 divides 1423 by NAT_4:9;
    1423 = 29*49 + 2; hence not 29 divides 1423 by NAT_4:9;
    1423 = 31*45 + 28; hence not 31 divides 1423 by NAT_4:9;
    1423 = 37*38 + 17; hence not 37 divides 1423 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1423 & n is prime
  holds not n divides 1423 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
