613 mitzvot, and the gematria of Taryag

Where the count of the commandments comes from, what it divides into, the words the tradition finds 613 in, and the prophets who gathered them down to one.

Six hundred and thirteen is the number of the commandments of the Torah, and its Hebrew name is nothing more than the number written in letters: tav, resh, yod, gimel, read as a word, taryag. The 613 mitzvot are among the best-known facts in Jewish life, and the count is older than any list of them. This page sets out where the number actually comes from, what it divides into, the words the tradition finds 613 hidden in, which is what most people mean by 613 gematria, and one count this site was able to check letter by letter against its own text.

תריג=613

Rabbi Simlai’s count

The number’s classic statement is near the end of tractate Makkot, and it is made as a teaching rather than as a list. Rabbi Simlai expounded: six hundred and thirteen commandments were said to Moshe, three hundred and sixty-five prohibitions, like the days of the solar year, and two hundred and forty-eight positive commandments, like the limbs of a person. Nobody on the daf enumerates them. Elsewhere the Gemara simply takes the number for granted. In Shabbat, explaining why Moshe broke the tablets, it has him reason that if the Pesach, which is one of the 613 commandments, is forbidden to an estranged Israelite, how much more the whole Torah.

Then Rav Hamnuna asks the question the Gemara asks of any teaching: which verse? And the verse he gives is one he names elsewhere as the first Torah a father teaches a child who has learned to speak.

תורה is six hundred and eleven in gematria. תורה=611 That is the Torah Moshe commanded us. The first two of the Ten Commandments, I am, and you shall have no other, we heard from the mouth of the Almighty Himself, and 611 and those two are 613.

Notice the order of events, because it is the order of almost every gematria the Talmud makes. The count comes first, as a received teaching; the verse is asked for afterwards, and the letters arrive to carry a number that was already known. The Rambam draws a halachic consequence from the answer. He opens his own enumeration, the Sefer HaMitzvot, with I am, and cites this very derivation as proof that belief in God is itself one of the 613, since it is one of the two the people heard directly. The piece on Ki Teitzei, the portion with the largest single share of the count, comes to the same arithmetic from the Rambam’s side.

Two hundred and forty-eight, and three hundred and sixty-five

The two halves of Rabbi Simlai’s number are each matched to something that can be counted. Three hundred and sixty-five is the solar year. Two hundred and forty-eight is the Mishnah’s own count of the limbs of the body, given in tractate Oholot bone by bone: thirty in the foot, thirty in the hand, eighteen vertebrae in the spine, and so on, a hundred and one on one side and a hundred and one on the other, until the total comes to two hundred and forty-eight. It is an anatomy of the Mishnah’s own, reckoned for the laws of impurity, and it should not be set against a modern count of bones.

The tradition then finds 248 in words, twice. Rami bar Abba, in Nedarim, reads the change of Avram’s name. At first the Holy One made him king over two hundred and forty-three limbs, and in the end over two hundred and forty-eight, the five added being the two eyes, the two ears and the organ of the covenant.

אברם=243אברהם=248

The difference is the heh, and a heh is five. Reish Lakish, in Moed Katan, finds the same number somewhere harder, in a ban: as it enters through two hundred and forty-eight limbs, so it leaves through two hundred and forty-eight. It enters because Yehoshua calls the city a חרם, a thing devoted, and it leaves because Chavakuk prays that in anger God remember רחם, compassion. The two words are the same three letters in a different order.

חרם=248רחם=248

The 613 gematria: three words, and the help one of them needs

Three words carry the number in the tradition’s own sources, and this site holds Rashi’s comment on each of them.

The fringes. On the verse that says the fringe is for remembering all the commandments, Rashi, following the Midrash Tanchuma, explains how: ציצית is six hundred, and its eight threads and five knots bring it to six hundred and thirteen. Bamidbar Rabbah, in a long run of counted readings, records the same sum as a baraita.

ציצית=600 The sum needs the word spelled with both its yods, which is how it is written today and not quite how the Torah writes it; the Ki Teitzei piece counts both spellings.

Yaakov’s message. Sending word to Esav, Yaakov says גרתי, I have sojourned with Lavan. Rashi’s second reading: the word is six hundred and thirteen, as if to say, I lived with Lavan and kept the 613 commandments, and did not learn from his wicked ways.

גרתי=613 Rashi does not say it, but anyone who sets the two words side by side can see why the value is exact. The four letters of גרתי are the four letters of תריג, in a different order. The article on the Baal HaTurim follows the word to the only other verse in the Tanakh that spells it this way.

The incense. Each prince of the tribes brings a golden pan full of incense. Bamidbar Rabbah reads the pan as the tablets, its ten shekels of gold as the Ten Commandments written on them, and the incense filling it as the 613 commandments mixed into those ten. Rashi gives the arithmetic, and he gives it honestly: קטרת comes to 613 only if its kuf is exchanged for a dalet, by the alphabet folded in half that the tradition calls atbash.

קטרת=709דטרת=613

That is worth dwelling on for a moment, because it is the tradition marking its own seams. The word does not come to 613 as written. It comes to 613 after one letter is exchanged by a named rule, and both the midrash and Rashi state the rule out loud rather than hiding the step. The article on the seven methods explains the exchange. The same page of Bamidbar Rabbah that gives the fringes their sum also sets יראת, fear, beside the Torah: both are six hundred and eleven. יראת=611

Six hundred and thirteen letters, and seven more

On the same verse of the incense, Bamidbar Rabbah makes a claim of a different kind, one that is not a gematria at all but a count. From I am to that is your neighbour’s, the first word of the Ten Commandments to the last, there are six hundred and thirteen letters, corresponding to the 613 commandments, and seven more, corresponding to the seven days of creation: six hundred and twenty in all.

This is the kind of claim a complete index can check, so it was checked. Adding up every letter from the first word of Shemot 20:2 to the last word of Shemot 20:17, in the verse numbering our text uses, our index counts 620. The midrash’s figure is exact, letter for letter, in the Westminster Leningrad Codex, and it fits the tablets as Shemot gives them. The version Moshe repeats in Devarim, with its added clauses, runs from its own I am to its own that is your neighbour’s in 708 letters, which the midrash’s figure does not fit.

Who made the list

The Talmud gives the number and does not give the list, and every list of the 613 is the work of a later enumerator deciding what counts as one commandment. The Rambam’s is the most influential: his Sefer HaMitzvot, and the count at the head of the Mishneh Torah, set out 248 positive commandments and 365 prohibitions. The Sefer HaChinuch arranges the same count portion by portion through the Torah, beginning with the first commandment in Parashat Bereshit, and this site’s list of the 613 mitzvot gives both: 613 in the Chinuch’s order, 248 positive and 365 negative, and the Rambam’s in his. Other enumerators, earlier and later, divide some verses differently at the margins, and their books are not in this site’s library. They all set out to reach the same total, because the total was the Gemara’s before any of them began.

Down to one

The Gemara in Makkot does not leave the number standing. Straight after Rav Hamnuna’s verse it tells how the prophets gathered the commandments into fewer and fewer principles. David came and set them on eleven, in the fifteenth psalm. Yeshayahu set them on six. Michah set them on three.

Yeshayahu came again and set them on two: keep justice, and do righteousness. Amos set them on one, seek Me and live, and Rav Nachman bar Yitzchak objects that seeking might mean seeking in the whole of the Torah. So the Gemara ends with Chavakuk, who set them on one.

Between the eleven and the six the same daf keeps a small scene. When Rabban Gamliel reached the end of David’s psalm, he who does these things shall never be moved, he would weep: the one who does all of them will not be moved, but the one who does only one of them will. The sages answered him that the verse says does these, not does all these; even one of them is enough.

That is the shape of the tradition’s whole relationship with the number. It counted the commandments and held the count as something received, found the number in the Torah’s own name, in the fringes, in a word Yaakov spoke and in the letters of the tablets, and then spent a page of Gemara showing that the count was not the point. The index behind this site finds 613 in 68 words, 931 runs of words and one whole verse of the twenty-four books. The reason any of them matters is that the tradition first said what 613 is.