
theorem
  1429 is prime
proof
  now
    1429 = 2*714 + 1; hence not 2 divides 1429 by NAT_4:9;
    1429 = 3*476 + 1; hence not 3 divides 1429 by NAT_4:9;
    1429 = 5*285 + 4; hence not 5 divides 1429 by NAT_4:9;
    1429 = 7*204 + 1; hence not 7 divides 1429 by NAT_4:9;
    1429 = 11*129 + 10; hence not 11 divides 1429 by NAT_4:9;
    1429 = 13*109 + 12; hence not 13 divides 1429 by NAT_4:9;
    1429 = 17*84 + 1; hence not 17 divides 1429 by NAT_4:9;
    1429 = 19*75 + 4; hence not 19 divides 1429 by NAT_4:9;
    1429 = 23*62 + 3; hence not 23 divides 1429 by NAT_4:9;
    1429 = 29*49 + 8; hence not 29 divides 1429 by NAT_4:9;
    1429 = 31*46 + 3; hence not 31 divides 1429 by NAT_4:9;
    1429 = 37*38 + 23; hence not 37 divides 1429 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1429 & n is prime
  holds not n divides 1429 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
