**Appendix B - The
parameter coefficients revisited.**

A number of additional comments may be made with reference to
the parametric formula that generates **G** (the
first eight words of the Bible), thus:

**[1]** - The three parameters (**500**,
**105**, and **99**) have substantial
geometrical links with the first two perfect numbers (**6**
and **28**), and with one another - as Figure A5
confirms:

**[2]** - For convenience, the parametric
equation and table of parameter coefficients are reproduced here:

We observe that over the range (ie omitting the triplet associated with the first, 913)

the p-values (coefficients of the first parameter,

**500**) are**constant**the q-values (coefficients of the second parameter,

**105**) vary from**-3 to 1**the r-values (coefficients of the third parameter,

**99**) vary from**-3 to 0**

It follows that the eight **G**-values
(highlighted) represent a subset of the set of 17 positive
integers obtained by allowing the coefficients to move freely
within these limits, thus:

**86**, 92, 98, 185, 191, 197, **203**,
290, **296**, **302**, 308, **395**,
**401**, **407**, 500, 506, 605

Given the limiting values 86 and 605, the
probability of a number chosen at random achieving a 'hit' is
17/520, or 0.03269. To select seven of the set* in succession *is
therefore associated with a probability of (0.03269)^7 -
equivalent to odds of 25 billion to one against! It is therefore
abundantly clear that these relationships could hardly have
arisen by chance!

**[3]** - And what of **913 **-
the number represented by the first Hebrew word of Holy
Scripture? As has already been observed, it is different *in
kind* from the following seven - its strategic position being
peculiarly marked in this manner. So what probability can be
associated with this? We take our lead from the geometrical
considerations which attend **G**: the sum of the
first seven, and the sum of the eight, were intended (most
appropriately, in view of the triangular pedigree of the
parameters!) to yield triangular numbers. This matter is now
considered. Because

we seek a positive integer (k, say) such that both (k + 1788) and (k + 2090) are triangular. A GW-BASIC search reveals k = 913 as the only solution - and along with it the eye-catching features of the triangles, 2701 and 3003, and the triplet of the uniquely-triangular, 666 - all matters which have been dealt with in earlier pages! Clearly then, this particular number is an essential feature of the overall design.

**[4]** - The table of coefficients
reveals a further interesting feature, viz the triplet of unit
magnitude relating to **296 **- the 7th Hebrew word
word and last of Genesis 1:1. It follows that any multiple of 296
will be represented by a triplet of the form, (m, -m, -m) - where
m is the multiplier. Additional features of interest follow:

attention has already been drawn to the fact that the name "Jesus" - as rendered in NT Greek, nominative case - is also the number 888, or 3 x 296; it would therefore appear in our table of coefficients as (3, -3, -3);

similarly, since the title "Christ" is 1480, or 5 x 296, it would appear as (5, -5, -5);

and finally, their combination, (8, -8, -8), would represent 2368 - "Jesus Christ"; interestingly, this repetition of eights is an image of 888, "Jesus"!

**[5]** - There is a further
extra-biblical observation: it is to do with the 'friendly' or
'amicable' number pair, **1184/1210 - **strangely
overlooked for many centuries by those searching for further
examples of the phenomenon. The feature that binds such numbers
together is the fact that each is the sum of the proper divisors
of the other. Now the *proper divisors* of a given number
are all the numbers, smaller than itself (including 1), which
divide it exactly. Thus, the proper divisors of 1184 are (1, 2,
4, 8, 16, 32, 37, 74, 148, 296, and 592 - their sum being 1210;
those of 1210 are (1, 2, 5, 10, 11, 22, 55, 110, 121, 242, and
605) - their sum, 1184. This number, 4 x 296, is the arithmetic
mean of the Lord's name and title, 888 and 1480. In our table of
parameters it would appear as (4, -4, -4).

**[6]** - It may be noted that the
entry (1, 1, 1) represents the straight sum of the parameters, ie
500 + 105 + 99 =** 704**, or **11 x 64**.
Intriguingly, this number leads us to 407 (the 6th of **G**)
in three distinct ways: (a) by writing its digits in reverse; or
(b) by summing the cubes of its digits; or (c) by subtracting 297
(= 3 x 99 - the length of an A4 sheet in mm). Factorising **407 **we obtain **11 x 37**
- and** **we observe that the** **factors
accompanying 11 in these expansions, viz 64 and 37, are those of
2368, "Jesus Christ".

**[7]** - We began this particular
line of investigation with the number **1260**.
Observing that this number is 12 x 105, we can write it as the
triplet of coefficients (0, 12, 0). Its close companion in the
Book of Revelation,** 666**, is likewise (0, 12,
-6).

**[8]** - Finally, it is worth
observing that the foregoing parametric equation is capable of
generating an infinite number of copies of **G**!
This may be deduced from the evaluation of the coefficient triple
**(3, -19, 5)**, ie (3 x 500 - 19 x 105 + 5 x 99) =
0! Clearly therefore, following vector principles, the
addition/subtraction of this triple to/from any other can have no
effect on the value generated. As an illustration of this,
consider the triple (1, 1, 1) which as we have seen generates the
value 704. The addition of (3, -19, 5) yields (4, -18, 6) - this
also generating 704!

Vernon Jenkins

27.1.00