My actual personal record so far (I hope to find 0.999x and 0.9999 ones soon):
Periapsis at 0.008684 AU (This is pretty darn close!), apoapsis at 13.35 AU.
This one is orbiting a Brown Dwarf. Look at that orbital period...
Periapsis at 0.81 AU, apoapsis at 28.75 AU.