Full of Years–A Mathematical Excursion with the Patriarchs

As we learn in Genesis, the patriarchs of the Hebrew nation lived to ripe old ages. Abraham passed on at 175 (Genesis 25:7). Isaac was 180 when he died (Genesis 35:28). The next generation, Jacob, lived to age 147 (Genesis 47:28), while Jacob’s most celebrated son, Joseph made it to 110 (Genesis 50:26).
Aside from the fact that these men would have almost single-handedly bankrupted the Social Security system had they lived in the United States, what can we learn from these numbers?
The bit of mathematical conjuring that follows is certainly not original to me, but its origin is, from my research, obscure. Let’s look.

Within the Ages

Looking at those credibility-stretching ages, we see that each of the first three can be expressed by a formula: Age=X * Y2. In other words, each each age is a multiple of a perfect square. What are the odds of that happening by coincidence? I checked out every age from 1 to 184, dividing each by the numbers 2 through 9. That is 1,472 possible combinations. And of those 1,472 possibilities, only 46 yielded perfect squares. That’s 3.1%. The likelihood of two generations in a row being like this? It’s less than one tenth of 1%, and the chances of three in a row matching are .0031%. That’s just north of 3 chances in 100,000–more likely than a lottery win but still very unlikely.

Not Just Unlikely But Following a Pattern

Looking more closely, not only do all three of those first three patriarchs have such X * Y2. ages, but there’s a pattern to their ages.
Let me demonstrate.
So if you noticed, the value of X decreases by 2 with each generation while the value of Y increases by 1 in the same generation. I’m not sure how to calculate the probability of that progression, but it is clearly far less probable than even the .0031% we saw above.

All that and 17 Also!

A great deal has been made by previous writers of the fact that this pattern also features all of the digits adding up to equal 17. When you think about it, however, that consistency is simply a feature of the progression. If X decreases by 2 and Y increases by 1 but is counted twice, then what else can that “Sum” column do but remain steady. Still, if there’s significance to the number 17, there might be something to it.
It turns out that 17 is a significant number for a couple reasons:
  • It is a prime number.
  • It is the seventh prime number: 1, 3, 5, 7, 11, 13, 17.
  • It is a combination of 7 (the number of the divine) and 10 (which appears several times in Genesis). E.W. Bullinger explains this sum as a combination of “spiritual perfection, plus ordinal perfection, or the perfection of spiritual order.”

Have We Forgotten Joseph?

I know that you’re wondering if Joseph, our fourth patriarch, fits the pattern. If the progression continued, then we would expect Joseph to be 1*(8*8) or 64 years old when he died. Instead, of course, he lived to be 110. So is Joseph the pattern buster?
Perhaps it is nothing but Joseph’s age can be expressed with the expected X (1) and the sums of the three preceding squared Ys (5, 6, and 7). That is, 1*(25+36+49)=110.
Of course, even though I suggested that might signify nothing, I don’t really believe it. What are the chances that happens by accident?
Let’s assume that we’re adding up three numbers hoping to reach 110. We could use dozens of different combinations if we didn’t care about those perfect squares. But if we restrict ourselves to perfect squares, there are only three combinations: 2 (4), 5 (25), and 9 (81) on one hand, and the 5,6, 7-combination noted above. In short, there is very little chance that Joseph’s age just happens to combine the squares that were found in the ages of his three preceding ancestors.

So What Does It All Mean?

Hopefully I have convinced you that the numerical play afoot in the ages of the patriarchs is not just an accidental occurrence. Assuming that it is not an accident leaves us with the sense that some intent lay behind these numbers.
The mere presence of these numbers does not prove anything about the interpretation of these numbers and it does not prove or disprove the hand of God in the creation of the Genesis text.
  • Could a human author have deposited mathematical Easter eggs for readers to discover? It’s possible.
  • Could God have controlled the ages of the patriarchs in order to produce these numbers? That’s possible as well.
Either way, what does it mean? That’s a question for a later post.

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