# Gaussian Primes and the Quran

We are at a historical juncture witnessing the monumental structure of the Qurans 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 lower-class 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 a2 + b2 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 19-based mathematics. Note the 10th Gaussian prime is the number 67 which also happens to be the 19th ordinary prime. But the relation between the indices is what is amazing.  You will note that the 10th initialed chapter in the Quran is 19.

Now let us go to the 19th Gaussian prime which is 151 and it happens to be the 36th ordinary prime. You will note that the 19th 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 47th Gaussian prime is the number 479 which happens to be the 92nd ordinary prime. The gematric value of the word Muhammad is 92 and chapter 47 in the Quran is also called Muhammad.

Finally 764th Gaussian prime is the 1514th 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 1273rd 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.