Shimon, known as Siamun Muran in the Japanese version, though not a priest, is a vizier of Pharaoh Atem. Solomon Muto is the modern day incarnation of Shimon. When Atem goes to the World of Memory, he initially confuses Shimon by calling him "Grandpa". The name "Siamun" is pronounced the same as "Shimon".
Shimon was originally one of the Pharaoh Akhenamkhanen's guardians, and he was granted the Millennium Key to hold. His Ka (or his monster spirit) that he summoned was "Exodia the Forbidden One" and he swore to seal it and never use it again after he destroyed the force that was attacking the Egyptian capital. He apparently gave up his position of guardian to Shada, and to him he relinquished the Millennium Key.
He plays a largely minor role in the Millennium World arc at first, as he introduces much of the ancient ways and terminology to the Pharaoh Atem.
When Zorc Necrophades rises and begins to march on the city, Shimon takes up the Millennium Key that Isis brought back and he summons Exodia to combat Zorc. Although Exodia experiences some success, especially after Siamun demonstrates its ability to regenerate after its arm was torn off by Zorc, Zorc overpowers Exodia because its power is based on Siamun's, while Zorc can draw power from the darkness. Therefore, Exodia is destroyed and Siamun is killed.
Paradox appears in Yu-Gi-Oh! Duel Monsters 4: Battle of Great Duelist as a first tier opponent. This time, he uses all low-level Normal Monsters, including a few previously used by Pegasus J. Crawford (albeit not used to their potential). Paradox's deck also contains the four limbs to Exodia (like Sugoroku Mutou), which he will not play, and cannot be completed without the fifth piece.
His ka is Exodia and his present day self Solomon Muto plays an Exodia Deck in World Championship 2004.
In episode 201 of the English dub, he says the phrase "So let it be written. So let it be done." This was taken from the (for lack of a better term) catchphrase of the Pharaoh Rameses II, played by Yul Brynner, in the epic film The Ten Commandments.