
theorem
  1039 is prime
proof
  now
    1039 = 2*519 + 1; hence not 2 divides 1039 by NAT_4:9;
    1039 = 3*346 + 1; hence not 3 divides 1039 by NAT_4:9;
    1039 = 5*207 + 4; hence not 5 divides 1039 by NAT_4:9;
    1039 = 7*148 + 3; hence not 7 divides 1039 by NAT_4:9;
    1039 = 11*94 + 5; hence not 11 divides 1039 by NAT_4:9;
    1039 = 13*79 + 12; hence not 13 divides 1039 by NAT_4:9;
    1039 = 17*61 + 2; hence not 17 divides 1039 by NAT_4:9;
    1039 = 19*54 + 13; hence not 19 divides 1039 by NAT_4:9;
    1039 = 23*45 + 4; hence not 23 divides 1039 by NAT_4:9;
    1039 = 29*35 + 24; hence not 29 divides 1039 by NAT_4:9;
    1039 = 31*33 + 16; hence not 31 divides 1039 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1039 & n is prime
  holds not n divides 1039 by XPRIMET1:22;
  hence thesis by NAT_4:14;
