
theorem
  5039 is prime
proof
  now
    5039 = 2*2519 + 1; hence not 2 divides 5039 by NAT_4:9;
    5039 = 3*1679 + 2; hence not 3 divides 5039 by NAT_4:9;
    5039 = 5*1007 + 4; hence not 5 divides 5039 by NAT_4:9;
    5039 = 7*719 + 6; hence not 7 divides 5039 by NAT_4:9;
    5039 = 11*458 + 1; hence not 11 divides 5039 by NAT_4:9;
    5039 = 13*387 + 8; hence not 13 divides 5039 by NAT_4:9;
    5039 = 17*296 + 7; hence not 17 divides 5039 by NAT_4:9;
    5039 = 19*265 + 4; hence not 19 divides 5039 by NAT_4:9;
    5039 = 23*219 + 2; hence not 23 divides 5039 by NAT_4:9;
    5039 = 29*173 + 22; hence not 29 divides 5039 by NAT_4:9;
    5039 = 31*162 + 17; hence not 31 divides 5039 by NAT_4:9;
    5039 = 37*136 + 7; hence not 37 divides 5039 by NAT_4:9;
    5039 = 41*122 + 37; hence not 41 divides 5039 by NAT_4:9;
    5039 = 43*117 + 8; hence not 43 divides 5039 by NAT_4:9;
    5039 = 47*107 + 10; hence not 47 divides 5039 by NAT_4:9;
    5039 = 53*95 + 4; hence not 53 divides 5039 by NAT_4:9;
    5039 = 59*85 + 24; hence not 59 divides 5039 by NAT_4:9;
    5039 = 61*82 + 37; hence not 61 divides 5039 by NAT_4:9;
    5039 = 67*75 + 14; hence not 67 divides 5039 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5039 & n is prime
  holds not n divides 5039 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
