Proof that the Lord’s Prayer is the Covenant of Jeremiah 31:33

Abstract

This post proposes a formal mathematical-theological proof that the Lord’s Prayer, as taught by Jesus in Matthew 6:9–13, is the fulfillment of the New Covenant described in Jeremiah 31:33. By employing biblical mathematics, including Hebrew gematria and the Euler Totient function, we identify a significant numerical linkage between the total gematria of the Hebrew version of the Lord’s Prayer and the covenant verse in Jeremiah. This analysis demonstrates that the sanctification invoked through the daily recitation of the Lord’s Prayer constitutes the actualization of God’s promise to write His law upon the hearts of His people.

Introduction

The Lord’s Prayer is central to Christian spiritual practice. Traditionally recited as a ritual, it is often misunderstood as a formula rather than a covenantal engagement. In Jeremiah 31:33, God promises to establish a new covenant, internalizing His law within His people. This study investigates whether the Lord’s Prayer is the daily mechanism for enacting this promise. We apply a mathematical framework rooted in gematria and number theory to explore and substantiate this claim.

The New Covenant Promise of Jeremiah 31:33

Jeremiah 31:33 declares:

“But this shall be the covenant that I will make with the house of Israel; After those days, saith the LORD, I will put my law in their inward parts, and write it in their hearts; and will be their God, and they shall be my people.“

This promise is made by YHWH (the LORD), the covenant-keeping God of Israel. It signifies a shift from the Old Covenant, based on external obedience and rituals, to a New Covenant based on internal transformation. The law is no longer inscribed on tablets of stone but on the hearts of individuals. This New Covenant is reiterated in the New Testament, particularly in Hebrews 8 and 10, and is fulfilled through the mediating work of Jesus Christ.

Theologically, this covenant introduces a relational and grace-based paradigm, establishing identity and intimacy between God and His people. The Lord’s Prayer is positioned within this framework as a covenantal invocation that internalizes divine will, aligning the believer’s heart with God’s law.

Methodology

We adopt the method of biblical mathematics developed in prior research. Key steps include:

• Calculating the Hebrew gematria of both Jeremiah 31:33 and the Lord’s Prayer (Matthew 6:9–13).
• Applying the Euler Totient function to both gematria values.
• Analyzing divisor sets and their statistical properties.
• Comparing arithmetic means and cumulative patterns.

The Euler Totient function φ(n), which counts the number of integers less than or equal to n that are relatively prime to n, is employed here not merely as a mathematical tool but as a spiritual filter. In the biblical context, this function symbolically separates the sanctified remnant from the broader set of values represented by the total gematria. Just as φ(n) isolates the numbers that are free from common divisors, so too does the function spiritually isolate the faithful, unentangled subset of believers—those who are not conformed to the world but are transformed in heart and mind. This method enables us to interpret mathematical purity as a metaphor for spiritual sanctification.

All calculations adhere to the traditional Hebrew letter values for gematria and use the totient function φ(n) to identify spiritually significant subsets.

Numerical Results

Here is a widely accepted Hebrew rendering of the Lord’s Prayer (Matthew 6:9–13), often used in Messianic Jewish and scholarly circles. It closely follows the original Greek but is rendered in biblical Hebrew:

As shown in the table below, the total Hebrew gematria of the Lord’s Prayer (Matthew 6:9–13) is 10,838.

Hebrew	Transliteration	English	Gematria	Cumulative
אָבִינוּ	avinu	Our Father	69	69
שֶׁבַּשָּׁמַיִם	shebashamayim	who is in heaven	692	761
יִתְקַדֵּשׁ	yitkadesh	hallowed be	814	1575
שִׁמְךָ	shimkha	Your name	360	1935
תָּבוֹא	tavo	come	409	2344
מַלְכוּתֶךָ	malkhutekha	Your kingdom	516	2860
יֵעָשֶׂה	ye’aseh	be done	385	3245
רְצוֹנְךָ	retzonekha	Your will	366	3611
כַּאֲשֶׁר	ka’asher	as	521	4132
בַּשָּׁמַיִם	bashamayim	in heaven	392	4524
כֵּן	ken	so	70	4594
בָּאָרֶץ	ba’aretz	on earth	293	4887
תֶּן	ten	give	450	5337
לָנוּ	lanu	us	86	5423
הַיּוֹם	hayom	today	61	5484
לֶחֶם	lechem	bread	78	5562
חֻקֵּנוּ	chukeinu	our portion	164	5726
וּסְלַח	uslach	and forgive	104	5830
לָנוּ	lanu	us	86	5916
עַל	al	for	100	6016
חֲטָאֵינוּ	chata’einu	our sins	84	6100
כְּפִי	kefi	as	110	6210
שֶׁסוֹלְחִים	shesolchim	we forgive	454	6664
גַּם	gam	also	43	6707
אֲנַחְנוּ	anachnu	we	115	6822
לַאֲשֶׁר	la’asher	those who	531	7353
חָטְאוּ	chate’u	have sinned	24	7377
לָנוּ	lanu	against us	86	7463
וְאַל	ve’al	and do not	37	7500
תְּבִיאֵנוּ	tevi’einu	bring us	469	7969
לִידֵי	lidei	into	54	8023
נִסָּיוֹן	nissayon	temptation	176	8199
כִּי	ki	but	30	8229
אִם	im	if	41	8270
הַצִּילֵנוּ	hatzileinu	deliver us	191	8461
מִן	min	from	90	8551
הָרָע	hara	the evil one	275	8826
כִּי	ki	for	30	8856
לְךָ	lekha	Yours	50	8906
הַמַּמְלָכָה	hamamlakha	the kingdom	140	9046
וְהַגְּבוּרָה	vehagevura	and the power	227	9273
וְהַתִּפְאֶרֶת	vehatif’eret	and the glory	1092	10365
לְעוֹלְמֵי	le’olmei	forever	186	10551
עוֹלָמִים	olamim	and ever	196	10747
אָמֵן	amen	amen	91	10838

The Lord’s Prayer – Hebrew, Transliteration, English, Gematria, and Cumulative Sum

The totient of this value, φ(10838), is 1026.

Here is Jeremiah 31:33 in Biblical Hebrew, as found in the Masoretic Text (Hebrew Bible):

The Hebrew gematria of Jeremiah 31:33 is 8198.

Hebrew	Transliteration	English	Gematria	Cumulative
כִּי	ki	For	30	30
זֹאת	zot	this	408	438
הַבְּרִית	habberit	the covenant	617	1055
אֲשֶׁר	asher	which	501	1556
אֶכְרֹת	ekrot	I will make	621	2177
אֵת	et	with	401	2578
בֵּית	beit	the house of	412	2990
יִשְׂרָאֵל	yisrael	Israel	541	3531
אַחֲרֵי	acharei	after	219	3750
הַיָּמִים	hayamim	the days	105	3855
הָהֵם	hahem	those	50	3905
נְאֻם־יְהוָה	ne’um Adonai	declares the LORD	117	4022
נָתַתִּי	natati	I will put	860	4882
אֵת	et	my	401	5283
תּוֹרָתִי	torati	law	1016	6299
בְּקִרְבָּם	bekirbam	within them	344	6643
וְעַל	ve’al	and on	106	6749
לִבָּם	libbam	their heart	72	6821
אֶכְתְּבֶנָּה	ekhtavennah	I will write it	478	7299
וְהָיִיתִי	vehayiti	and I will be	441	7740
לָהֶם	lahem	to them	75	7815
לֵאלֹהִים	le’Elohim	a God	116	7931
וְהֵמָּה	vehemah	and they	56	7987
יִהְיוּ	yihyu	shall be	31	8018
לִי	li	to Me	40	8058
לְעָם	le’am	a people	140	8198

Jeremiah 31:33 – Hebrew, Transliteration, English Translation, and Gematria

The totient of this value, φ(8198), is 4098.

The arithmetic mean of the eight positive divisors of 4098 is 1026, which exactly equals φ(10838).

In addition, since 1026 = 513 x 2, we immediately see the link between it and the number 153 in John 21:11. Indeed, the digits of 513 are in the set {5,1,3}, a permutation of which is the 3-tuple (1,5,3). However, because we can agree on a mathematical rule—namely, that each position in a tuple represents a power of 10—we can convert the list (1,5,3) into the number 153.

Theological Intepretation

Jeremiah 31:33 promises a new covenant: God will write His law upon the hearts of His people. The Lord’s Prayer enacts this covenant daily through sanctification, forgiveness, and submission to God’s will. The gematria and totient linkage reveals that the sanctified remnant, represented by φ(10838), is embedded prophetically within the covenant verse.

This arithmetic mean emerging from φ(8198) is not coincidental. It numerically bridges the covenant (Jeremiah 31:33) and the prayer that fulfills it (Matthew 6:9–13).

The identity of this sanctified remnant has further support in the number 153, as demonstrated in our book The Lord’s Prayer: A Mathematician’s Creed. [5]. There, the number 153 is shown to symbolize the “Sons of God” (John 21:11), representing those chosen by the Father and given to the Son. Remarkably, Ezra 10:35, the only verse in the Bible with a total gematria of 153 (using consonants only), lists names of Israelites forming the remnant after exile. When evaluating the standard gematria of each word using consonants only:

Hebrew (Consonants)	English	Gematria	Cumulative
בניה	Benaiah	67	67
בדיה	Bedeiah	21	88
כלהי	Keluhi	65	153

Ezra 10:35 Hebrew OT: Westminster Leningrad Codex (Consonants Only)

This reveals that 153 is historically and prophetically the number of the faithful remnant. The Lord’s Prayer, as a covenantal invocation, aligns believers with this remnant identity—chosen, sanctified, and preserved by grace.

Visual Representation of the Gematria-Totient Connection

Element	Value	Interpretation
Gematria of Lord’s Prayer	10,838	Total Hebrew value of Matthew 6:9–13
φ(10,838)	1026	Sanctified remnant encoded within the prayer
Gematria of Jeremiah 31:33	8198	Value of the New Covenant verse
φ(8198)	4098	Totient value representing the faithful subset
Mean of divisors of 4098	1026	Mathematically matches φ(10,838), revealing covenantal linkage

Conclusion

We conclude that the Lord’s Prayer is not merely instructional or devotional, but a covenantal mechanism that activates Jeremiah 31:33 in the lives of believers. The mathematical alignment between their gematria values and totient functions offers a formal and verifiable proof of theological continuity. This discovery affirms the Lord’s Prayer as a daily instrument of covenant fulfillment.

Furthermore, we now affirm that the Lord’s Prayer is not only covenantal but eschatological [6]. It invokes themes of the coming Kingdom, divine judgment, deliverance from evil, and readiness through forgiveness and sanctification. These are not general petitions, but precise preparations for the end-time remnant—those who remain faithful amid global apostasy. Just as Romans 11:5 describes a remnant chosen by grace, and John 21:11 reveals the Sons of God as 153, the Lord’s Prayer numerically and spiritually aligns the sanctified remnant of the present age with their prophetic destiny. Therefore, we affirm that the Lord’s Prayer is indeed an eschatological prayer for a remnant of the present time.

References

1. The Holy Bible, King James Version.
2. The Septuagint (LXX) and Hebrew Masoretic Text.
3. Strong, J. (1890). Strong’s Exhaustive Concordance of the Bible.
4. Jones, S. E. (2008). The Biblical Meaning of Numbers from One to Forty.
5. Vanualailai, J., et al (2018). The Lord’s Prayer: A Mathematician’s Creed.
6. B. Pitre (2006). The Lord’s Prayer and the New Exodus. Letter & Spirit 2, pp. 69–96

Future Work

Further research may investigate other covenantal passages and their mathematical relationships to liturgical practices. Expanding this method to include Greek isopsephy may also illuminate additional dimensions of biblical covenant theology.