Rav Shimon Kayara רב שמעון קיירא

Rabbi Simlai said the commandments are 613, but left no list. The first to undertake to enumerate them by name was Rav Shimon Kayara in Halakhot Gedolot—a great code of law compiled in Babylonia about the year 4600.

Halakhot Gedolot is the second book of the age after the Sheiltot and the first that tries to take in the halakhah as a whole: the ruling is drawn out of the Talmud, the disputes removed, the order by subject. The Ashkenazi academies held to it for centuries; Rashi and the Tosafists cite it as "BaHaG".

And the count of the commandments became a field of great argument. Rambam, writing three centuries later, opens the Sefer haMitzvot with a direct critique: the author of Halakhot Gedolot counted as commandments what are not commandments—rabbinic ordinances, particulars, generalisations. Ramban in reply rose to the defence of Halakhot Gedolot. So one Gaon's book set going a dispute that is alive to this day.

The years are taken from the Epistle of Rav Sherira Gaon—the letter of 4747 (987), the only source in which the age of the Savoraim is set out by name and year. There is no other testimony, and that should be kept in mind.