
theorem
  1493 is prime
proof
  now
    1493 = 2*746 + 1; hence not 2 divides 1493 by NAT_4:9;
    1493 = 3*497 + 2; hence not 3 divides 1493 by NAT_4:9;
    1493 = 5*298 + 3; hence not 5 divides 1493 by NAT_4:9;
    1493 = 7*213 + 2; hence not 7 divides 1493 by NAT_4:9;
    1493 = 11*135 + 8; hence not 11 divides 1493 by NAT_4:9;
    1493 = 13*114 + 11; hence not 13 divides 1493 by NAT_4:9;
    1493 = 17*87 + 14; hence not 17 divides 1493 by NAT_4:9;
    1493 = 19*78 + 11; hence not 19 divides 1493 by NAT_4:9;
    1493 = 23*64 + 21; hence not 23 divides 1493 by NAT_4:9;
    1493 = 29*51 + 14; hence not 29 divides 1493 by NAT_4:9;
    1493 = 31*48 + 5; hence not 31 divides 1493 by NAT_4:9;
    1493 = 37*40 + 13; hence not 37 divides 1493 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1493 & n is prime
  holds not n divides 1493 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
