This appendix supplies the textual distinctions and arithmetic behind the main explanation. MT means Masoretic Text and LXX Septuagint. The date examples retain the normal Nisan, 430-years-in-Egypt, no-additional-60-for-Terah framework. The sole change between each paired table is the expressly restored second Cainan.
Go directly to: Textual witnesses · Regular dates · Cumulative coordinates · Creation boundaries · Calculations · Sources.
1. The name and the numbers
| Witness | Local genealogical order, ancestor to descendant | What it supplies here |
|---|---|---|
| MT Genesis 11:12–13 | Arphaxad → Shelah | Arphaxad’s 35 years before Shelah and 403 afterward: 438 total |
| LXX Genesis 11:12–13, Brenton’s edition | Arphaxad → Cainan → Sala | Cainan’s 130 years before Sala and 330 afterward: 460 total |
| Luke 3:35–36, BSB | Arphaxad → Cainan → Shelah, read forward | The genealogical name and position; no begetting ages or lifespans |
Direct readings: MT-based Genesis 11:12–13, BSB; Greek Genesis in Brenton; Luke 3:35–36, BSB.
“Second Cainan” distinguishes this post-Flood figure from Kenan, son of Enosh, in Genesis 5:9–14, BSB. Luke’s BSB text uses Cainan for that earlier name too (Luke 3:37–38). Counting the post-Flood Cainan does not add a second copy of the earlier Kenan.
The comparison uses the LXX Cainan figures inside an otherwise MT calculation. It does not import all the LXX ages. In particular, Arphaxad remains 35 + 403 = 438, and Shelah remains 30 + 403 = 433. Brenton’s Greek Genesis has different Arphaxad figures; its variant note must not be mixed into the MT rows below. The quoted edition is named because Greek witnesses and translations require individual checking.
2. Regular MT: inserting 130 years
These are ordinary birth coordinates within the stated chronological reconstruction. Later anchors are held fixed, and earlier dates are calculated backward. BC dates decrease as time moves forward.
| Birth node | Normal MT, BC | MT with restored Cainan, BC |
|---|---|---|
| Arphaxad | 2456 | 2586 |
| Second Cainan | — | 2551 |
| Shelah | 2421 | 2421 |
| Eber | 2391 | 2391 |
Normal chain: 2456 − 35 = 2421; 2421 − 30 = 2391.
Restored chain: 2586 − 35 = 2551; 2551 − 130 = 2421; 2421 − 30 = 2391.
The restored Cainan’s ordinary lifespan is 2551–2091 BC, since 2551 − 460 = 2091. His death is not the next birth in the regular chain. Shelah has already been born 330 years earlier, in 2421 BC.
The normal Arphaxad date 2456 BC remains the baseline. 2586 BC belongs only to the explicitly restored-Cainan comparison. Neither the default MT dates nor the native LXX table is silently changed.
Source: File 18 §1.6.2 and author clarification 12A; the normal MT regular rows and the full-430 application supply the unchanged downstream anchors. Full regular chronology tables.
3. Cumulative MT: inserting 460 years
The cumulative method adds complete lives along the ancestral line backward from Moses’ death/Conquest at 1406 BC. These BC labels identify positions in that mathematical arrangement. They are not ordinary birth dates.
The following table uses the canonical Moses-line Nisan column. The wider seven-year envelopes remain separately listed in File 18; no change of endpoint is needed for this example.
| Cumulative node | Normal MT, BC | MT with restored Cainan, BC |
|---|---|---|
| Arphaxad | 4831 | 5291 |
| Second Cainan | — | 4853 |
| Shelah | 4393 | 4393 |
| Eber | 3960 | 3960 |
Normal chain: 4831 − 438 = 4393; 4393 − 433 = 3960.
Restored chain: 5291 − 438 = 4853; 4853 − 460 = 4393; 4393 − 433 = 3960.
Shelah is again the point of convergence. The added 460-year interval shifts Arphaxad and earlier ancestors; it leaves Shelah and every later row unchanged.
The full ancestral chain consequently changes from 26 lifespans totaling 12600 years to 27 lifespans totaling 13060 years:
12600 + 460 = 13060; 1406 + 13060 = 14466 BC.
Source: File 18 §§6A–6B, with File 09 §3A.1 for the cumulative variant controls. Full unrounded cumulative tables.
4. Comparing corresponding Creation boundaries
Normal MT places the symbolic Creation week at 4121–4114 BC, with Adam’s Year-6 position at 4116 BC. The corresponding cumulative week is 14011–14004 BC, with its Year-6 position at 14006 BC.
Adding Cainan moves the regular week back 130 years and the cumulative week back 460 years. Each row below matches the same position in the two weeks.
| Corresponding position | Regular MT, normal → restored, BC | Cumulative MT, normal → restored, BC |
|---|---|---|
| Week beginning | 4121 → 4251 | 14011 → 14471 |
| Adam, Year 6 | 4116 → 4246 | 14006 → 14466 |
| Week close | 4114 → 4244 | 14004 → 14464 |
All three normal comparisons give 9890 years. All three restored comparisons give 10220 years:
14471 − 4251 = 14466 − 4246 = 14464 − 4244 = 10220.
File 22 §5A.1 explicitly gives this matched-Cainan construction. Its further equality 10220 = 7 × 1460 opens a separate calendrical comparison in that section; the simple insertion mechanism is sufficient for the present article.
The 10320 comparison elsewhere in File 22 uses a different pairing: cumulative Cainan-restored Adam 14466 BC against regular apparent-age Adam 4146 BC (the separate +30 apparent-age overlay on 4116 BC). Its arithmetic is 14466 − 4146 = 10320. It must remain distinct from the matched-Cainan comparison above, which places Cainan in both chronologies and uses corresponding Year-6 positions.
For the original unrounded relationship, see Between Two Chronologies: The 9890-Year Bridge. The Rounded 9900-year article uses its own Rounded inputs.
5. The arithmetic at a glance
| Relationship | Calculation | Significance |
|---|---|---|
| Cainan’s whole life | 130 + 330 = 460 | Years before and after Shelah’s birth |
| Unequal additions | 460 − 130 = 330 | Post-fatherhood years enter only the cumulative sum |
| New separation | 9890 + 330 = 10220 | Corresponding Creation positions with Cainan in both methods |
| Key-of-23 measure | 460 = 20 × 23 | Exact factorization of the added lifespan |
These are exact calculations within named constructions. Further theological readings or arguments about the history of the textual traditions require their own evidence; the arithmetic alone does not establish a statistical probability or a historical cause.
6. Sources and further reading
- File 18, Chronological Data Tables: §1.6 explains the two insertion values; §§6A–6B give the cumulative tables; author clarification 12A fixes the restored Cainan’s regular date states.
- File 09, Cumulative Architecture: §3A.1 shows how the 460-year Cainan addition carries through the cumulative Creation envelope. The Moses-line column used here remains distinct from the Aaron-line and seasonal alternatives.
- File 22, Cumulative MT Harmonics: §5A.1 controls the 10220 comparison; §7.2 supplies the separately qualified 10320 comparison; §6.1 develops the Cainan/Watcher relationships beyond this introduction.
- Canonical source index and original extended discussion.
Scripture quotations: Berean Standard Bible (BSB), public domain. Biblical readings are identified by passage and edition. Brenton Septuagint Translation: public domain, as identified. See the Brenton edition information. Calculations are presented separately from translation wording.