
theorem
  2039 is prime
proof
  now
    2039 = 2*1019 + 1; hence not 2 divides 2039 by NAT_4:9;
    2039 = 3*679 + 2; hence not 3 divides 2039 by NAT_4:9;
    2039 = 5*407 + 4; hence not 5 divides 2039 by NAT_4:9;
    2039 = 7*291 + 2; hence not 7 divides 2039 by NAT_4:9;
    2039 = 11*185 + 4; hence not 11 divides 2039 by NAT_4:9;
    2039 = 13*156 + 11; hence not 13 divides 2039 by NAT_4:9;
    2039 = 17*119 + 16; hence not 17 divides 2039 by NAT_4:9;
    2039 = 19*107 + 6; hence not 19 divides 2039 by NAT_4:9;
    2039 = 23*88 + 15; hence not 23 divides 2039 by NAT_4:9;
    2039 = 29*70 + 9; hence not 29 divides 2039 by NAT_4:9;
    2039 = 31*65 + 24; hence not 31 divides 2039 by NAT_4:9;
    2039 = 37*55 + 4; hence not 37 divides 2039 by NAT_4:9;
    2039 = 41*49 + 30; hence not 41 divides 2039 by NAT_4:9;
    2039 = 43*47 + 18; hence not 43 divides 2039 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2039 & n is prime
  holds not n divides 2039 by XPRIMET1:28;
  hence thesis by NAT_4:14;
end;
