kohen priest - Can any kohanim trace all the way back to Aaron?

Can any kohanim alive today trace their lineage all the way back to the High Priest Aaron? If not, who can go the farthest?

Answer

There are a couple of families listed in the Kohen's Handbook that can in fact trace their lineage back to Aaron. The Rappaport family being the most famous. The Rappaports if I am not mistaken trace their lineage back to Tzadok(As can a couple of other families). There is a Kohanic branch of the Azoulai family that can trace their lineage back to Itamar. I know of three different families that can trace their lineage back to Rabbi Yishmael.

In regards to BA's assertion that lineage is uncertain, especially amongst Sephardim where one is not automatically believed when he says he is a Kohen but that he has to prove lineage, this is only a doubt that there may have been a mamzer or something else such as that that mixed into the line, and thus there is reason to be extra-cautious(sorry don't remember the source in the Sh"A, but it is a basic machloket between the Mechaber and the Rema as to whether we can trust soemone to say they are a Kohen).