There are 365 negative commandments, corresponding to the number of days in a solar year, and 248 positive commandments, ascribed to the number of bones and significant organs in the human body. Babylonian Talmud, Makkot 23b-24a. As stated by the Jewish Virtual Library : "There is also complete agreement that these 613 mitzvot can be broken down into 248 positive mitzvot (one for each bone and organ of the male body) and 365 negative mitzvot (one for each day of the solar year)." Though the number 613 is mentioned in the Talmud, its real significance increased in later medieval rabbinic literature, including many works listing or arranged by the mitzvot.
Some rabbis declared that this count was not an authentic tradition, or that it was not logically possible to come up with a systematic count. Not surprisingly, no early work of Jewish law or Biblical commentary depended on the 613 system, and no early systems of Jewish principles of faith made acceptance of this Aggadah (non-legal Talmudic statement) normative. The classical Biblical commentator and grammarian Rabbi Abraham ibn Ezra denied that this was an authentic rabbinic tradition. Ibn Ezra writes "Some sages enumerate 613 mitzvot in many diverse ways [2] but in truth there is no end to the number of mitzvot [3] and if we were to count only the root principles [4] the number of mitzvot would not reach 613" ( Yesod Mora , Chapter 2).
Source: Wikipedia > 613 Mitzvot
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