In our long quest for perfection in a deep mourning over numbers, we have reached perfection. But that perfection is not yet perfect. YHWH is absolute perfection. And I will reach perfection the day I will see my Lord Jesus-Christ of Nazareth face to face. On earth, we continue our journey in mourning for perfection. And I think we can do more. We can be more perfect. We can be more perfect than in « prime numbers (addendum 7) ». Therefore in this new article named « prime numbers (addendum 8) », we will look for more perfection by prophesying (talking) mathematically. We will look for more precision in the elien representation in base 3 and we will postulate some prime numbers sequences from the base 3 of the elien representation.
In the article « prime numbers (addendum 7) » we were in the base 3/2 or 2/3 of the elien representation and we find some prime numbers sequences. But it seems that the base 3/2 is not enough perfect suitable for our quest. We must find another base more suitable. And that base is the base 3. Let us remind the findings in base 3/2 with the appropriate correction:
First case B = 3(2x+1): x = (B – 3)/6
Second case B = (2x+1)(3y+1): y = E((-1+√B)/3) and x = E((-1/3+√(B/6)))
Third case B = (2x+1)(3y-1): y = E((1+√B)/3) and x = E((1/3+√(B/6)))
Now let us go in the base 3 of the elien representation. As the base is increasing there will be more cases. In the base 3 we will use just a combination of 3x, 3x-1 and 3x+1. We have just 5 combinations which are B = 3(3x-1), B = 3(3x+1), B = (3x – 1)(3y – 1), B = (3x + 1)(3y – 1) and B = (3x + 1)(3y + 1). Therefore we have 5 cases.
First case B = 3(3x-1): x = (B+3)/9
Second case B = 3(3x+1): x = (B-3)/9
Third case B = (3x – 1)(3y – 1): x = E((1+√B)/3) and y = E((1+√B)/3))
Fourth case B = (3x + 1)(3y – 1): A = {E((1+√B)/3) , E((-1+√B)/3)) }, x ∈ A and y ∈ A
Fifth case B = (3x + 1)(3y + 1): A = {E((-1+√B)/3) , E((-1+√B)/3)) }, x ∈ A and y ∈ A
Those 5 cases show the 5 manners how B can be written in the base 3 of the elien representation. Any given number B can be written at least according to one case with x and y specified above.
Thus we can have this simple prime number test. B is a prime number if B cannot be divided by 3 and if both E((-1+√B)/3) , E((1+√B)/3)) are odd integers.
Furthermore we can postulate these prime number sequences:
B = (3x – 1)(3y – 1) ± 1 with x and y are odd integers and B cannot divided by 3
B = (3x + 1)(3y – 1) ± 1 with x and y are odd integers and B cannot divided by 3
B = (3x + 1)(3y + 1) ± 1 with x and y are odd integers and B cannot divided by 3
In the essay « Prime number (addendum 9) » we will talk about the generalization of all this theory.
Maranatha !!!!! Come YHWH !!!!!!