We are at a historical juncture witnessing the
monumental structure of the Qurans Ultimate
Mathematics and how this mathematics relates to imaginary and complex numbers.
Carl
Friedrich Gauss was born in Brunswick
(Germany) on April 30th, 1777 and was the
only son of uneducated lowerclass parents. A story about his early education
demonstrates his unique gifts. While in elementary
school his teacher tried to occupy pupils by making them add up the integers from
1 to 100. The young Gauss produced the correct answer within seconds by a flash
of mathematical insight, to the astonishment of all. Gauss had realized that
pairwise addition of terms from opposite ends of the list yielded identical
intermediate sums: 1 + 100 = 101, 2 + 99 = 101, 3 + 98 = 101, and so on, for a
total sum of 50 Χ 101 = 5050. Gauss
contributions to the field of number theory and electricity and magnetisim are
invaluable. Without complex numbers, we would not have the knowledge to build
any of the modern electronic devices.
If
you pick up your calculator and punch in 1 and then punch the √ button
you will get an error, because the square root of a negative number is not
defined. However, in the complex plane we can draw an imaginary axis and have
imaginary numbers such as i, 2i, 3i, and so on. A complex number is the sum of
a real number and an imaginary number, such as (4 + i) or (5 + 3i). A Gaussian prime is a prime that could either
be complex or real and it is only divisible by itself, 1, 1 or i, i. A complex number of the form (a + bi) is a
Gaussian prime if and only if a^{2} + b^{2} is a prime.
Therefore, (4 + i) is a Gaussian prime, however, (4 + 3i) is not. The real Gaussian
primes are 3, 7, 11, 19
. , and are of the form (4n + 3), where n is any
integer including 0.
The
prime number 17, for example, is not a Gaussian prime since it can be factored
out into (4 + i)(4  i) = 17.
Now
let us tabulate all real Gaussian primes.
Gaussian Prime Index 
Ordinary Prime Index 
Real Gaussian Prime 
1 
2 
3 
2 
4 
7 
3 
5 
11 
4 
8 
19 
5 
9 
23 
6 
11 
31 
7 
14 
43 
8 
15 
47 
9 
17 
59 
10 
19 
67 
11 
20 
71 
12 
22 
79 
13 
23 
83 
14 
27 
103 
15 
28 
107 
16 
31 
127 
17 
32 
131 
18 
34 
139 
19 
36 
151 









47 
92 
479 









764 
1514 
12671 
Now let us see how these
numbers generate the Quranic 19based mathematics.
Note the 10^{th} Gaussian prime is the number 67 which also happens to
be the 19^{th} ordinary prime. But the relation between the indices is
what is amazing. You will note that the
10^{th} initialed chapter in the Quran is 19.
Now
let us go to the 19^{th} Gaussian prime which is 151 and it happens to
be the 36^{th} ordinary prime. You will note that the 19^{th}
initialed sura in the Quran
is 36. In a further observation, we note
that 151 assumed to be in base 9, is 127 in decimal system, again
generating that sura 9 has 127 verses.
The
47^{th} Gaussian prime is the number 479 which happens to be the 92^{nd}
ordinary prime. The gematric value of the word
Muhammad is 92 and chapter 47 in the Quran is also
called Muhammad.
Finally
764^{th} Gaussian prime is the 1514^{th} ordinary prime number.
Here we have this table actually generating the frequency of the word God in 9:127. Let us see how.
764
= 2 Χ2 Χ191
The
indices of the prime factors above are 1, 1 and 43.
1143
= 9 Χ127
The
number 1514 is a composite and its index is 1273. The reader can verify that
verse 9:127 in the Quran contains the 1273^{rd}
frequency of the word God.
This
number system is part of the Ultimate Mathematics of the Quran
and can only be authored by God alone.