THE ENNISA FORMULA The Secret
of Prime and Twin Prime Number Distribution The Laws of Prime ExclusionPART I and
Part II Originally
Published 1995 – Revised 11/11/2004 By Sollog
Immanuel AdonaiAdoni www.Sollog.com In this work I shall put forth a simple Euclidian Proof that
shows the infinite field of primes revolves around a Mod 90 Algorithm that
repeats infinitely throughout the infinite field of prime numbers. I show also give the first 6 rules to enable anyone to
quickly exclude most numbers from being prime. There are 3 more Prime Exclusion
rules that I will give in Part II of this work. The exclusion rules I am about to reveal narrows down the
potential field of prime candidates greatly, this should help in developing
prime testing programs that will run much more efficiently since the rules I am
putting forth exclude most numbers from being possible prime candidates. Primes are not Random the Prime Mod 90 Algorithm The first item I put forth in this work is the FACT that
prime numbers are not distributed randomly. There is absolutely a Mod 90
algorithm to prime numbers. The PROOF is available by using simple Euclidian
number observation via Base 9 Number Reduction incorrectly called by some
Theosophical Addition. Base 9 Number Reduction is a simple way to compress numbers
to their lowest integer from 1 to 9. You simply add the integers in any number
and keep repeating the task until you are left with 1 integer from 1 to 9. Ex:
129 = 1+2+9=12 and 12=1+2=3: so 129=3 via Base 9 Number Reduction. The following chart clearly shows the Mod 90 algorithm to
the distribution of primes. This algorithm appears in the hidden sequence of
numbers that Base 9 Number Reduction reveals. The total algorithm of the
reduced number sequence does not appear in only a Mod 30 sequence, the hidden
algorithm can only be fully seen if you use a Mod 90 chart. While a Mod 30 chart (which I use in Part
II) can reveal a simple pattern to primes where 8 prime columns are revealed,
it does not show the actual hidden algorithm that Base 9 Number Reduction
reveals. That number can only be shown via my Prime Mod 90 Chart. Here is my
Prime Mod 90 Chart.
COMPRESSED VALUE = Base 9
Reduction T = TWIN NP = NOT PRIME The Prime Mod 90 Chart shows how only 24 numbers are prime candidates in a 90 number field. The reason I must use 90 numbers to produce the 24 number prime sequence is the hidden Base 9 Number Reduction Algorithm does not reveal itself if I reduce this chart to say a Mod 30 Chart with an 8 number sequence. This hidden 24 number sequence is similar to the Fibonacci Sequence. If you chart the Fibonacci Sequence you will find a similar hidden Base 9 Number Reduction algorithm that also repeats after each 24^{th} Fibonacci Sequence. If you analyze the Prime Mod 90 chart you can also see how all primes greater than 7 fit into a Mod 30 Algorithm as well. However, the Base 9 Number Reduction algorithm does not reveal itself unless you view a Mod 90 chart. The FACT that a pattern of numbers (an algorithm) repeats over and over in the prime number sequence as my Prime Mod 90 chart shows is a simple Euclidian Proof that Prime Number Distribution IS NOT RANDOM. A Euclidian Proof simply means an observable pattern to numbers. It would be fairly easy to express this in an Algebraic expression as well, which is something most modern mathematicians would be used to doing. However, this work is intended for the masses and not just academics. The Prime Mod 90 Chart also shows all the locations where the infinite Twin Prime distribution field exists Once again the Prime Mod 90 Chart is a simple Euclidian Proof to two famous math questions, those being; are Twin Primes Random and are they infinite? The Prime Mod 90 Chart clearly shows 75% of Prime Candidates are also Twin Prime Candidates. So the clear answer is Twin Prime distribution is a repeating algorithm within the Prime algorithm in that it is a set field or constant within the field of prime candidates. The Prime Field Formula The following formula is true about where all prime candidates must exist, no prime can exist outside of this formula. Every prime number above 7 is located within the limited
field of whole integers expressed as 90(x) + n where x is a whole integer > 0 and n is equal
to one of the following numbers: 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61,
67, 71, 73, 77, 79, 83, 89, 91, 97 This can be reduced to Every prime number above 7 is located within the limited
field of whole integers expressed as 30(x) + n where x is a whole integer > 0 and n is equal
to one of the following numbers: 11, 13, 17, 19, 23, 29, 31, 37 These formulas do no PROVE that a number is prime, it merely
shows the very limited field where all prime candidates must exist. No prime
number can exist outside these very limited prime candidate fields. Now that I have shown exactly where all prime numbers have
to exist, I will give the first 6 of 9 Prime Exclusion laws that can be used to
quickly exclude primes. The first 6 Laws of Prime Exclusion The laws are 1.
Even number rule  All even numbers above 2 are not prime. 2.
Divisible by 5 rule  All numbers above 5 that end with a 5
are not prime. 3.
Repeating odd integer rule  A prime cannot have repeating odd integers ex: 777 etc. 4.
Number Reduction 3 remainder – An odd integer above 9 when
reduced cannot equal a remainder of 3. Ex: 21 = 2+1=3 5.
Number Reduction 6 remainder – An odd integer above 9 when reduced cannot equal a remainder of
6. Ex: 51 = 5+1=6 6.
Number Reduction 9 remainder – An odd integer above 9 when
reduced cannot equal a remainder of 9. Ex: 27 = 2+7=9 The Laws of Prime Exclusion Part II In The Laws of Prime Exclusion Part I, I gave 6 simple laws
to exclude numbers from being Prime. The laws are 1.
Even number rule  All even numbers above 2 are not prime. 2.
Divisible by 5 rule  All numbers above 5 that end with a 5
are not prime. 3.
Repeating odd integer rule  A prime cannot have repeating odd integers ex: 777 etc. 4.
Number Reduction 3 remainder – An odd integer above 9 when
reduced cannot equal a remainder of 3. Ex: 21 = 2+1=3 5.
Number Reduction 6 remainder – An odd integer above 9 when reduced cannot equal a remainder of
6. Ex: 51 = 5+1=6 6.
Number Reduction 9 remainder – An odd integer above 9 when
reduced cannot equal a remainder of 9. Ex: 27 = 2+7=9 In the next 30 Column table, you can see how every prime
neatly falls into one of 8 rows. Red number = PrimeGreen number = excluded number in Prime column
This table also shows exactly where every TWIN PRIME
will fall. It is the simplest Euclidian proof to show that Twin Primes repeat
infinitely. A proof for if Twin Primes are random and or infinite is
another mathematical question that man has been searching Millenniums for. The
Prime Mod 30 Chart clearly shows Twin Prime Candidates make up 75% of the
possible Prime Candidates in the Prime Mod 30 Chart. The 7^{th} Law of Prime Exclusion is the whole
square root exclusion rule. If an odd integer has a square root that is a whole
integer (which by the way must be a lower prime) that number is excluded. Ex:
49 the square root is a whole integer that being 7. 121 the square root is 11
and 169 the square root is 13. The 8^{th}
Law of Prime Exclusion is the Law of Exclusion for all nonprimes that don't
fall within the Mod 30 algorithm for Primes. This law is based on the fact that
all primes above 7 are located in a Mod 30 field of distribution. The only non
Primes left in this small field of prime number distribution are prime number
candidates that are within the Mod 30 Prime algorithm, but are factors of
smaller prime numbers and therefore excluded. These are a small amount of
numbers compared to the large amount of numbers that are generally excluded
with this rule! The 8^{th} Law of Prime Exclusion is stated as: If you subtract NINE from any whole integer above NINE,
and then divide by 30 and the result is a remainder of 2, 4, 8, 10, 14, 20, 22,
28 such numbers are prime candidates. If a number doesn't have one of these 8
numbers as a remainder, you can EXCLUDE it 100% from being prime. The 9^{th} Law of Prime Exclusion is the final test
to determine if a number is prime. The purpose of the first 8 Prime Exclusion
Laws is to enable a person to quickly determine the likelihood that a number is
a possible prime candidate and to QUICKLY EXCLUDE most numbers as being
possible prime candidates. The first 8 Laws cannot determine 100% that a number
is prime. The final exclusion rule of primes determines absolutely if a number
is prime. The final rule is testing an odd number above 89 for equal prime
factoring by primes below the square root of a number and greater than 5. Ex: 91 is the first number that is not
easily disqualified from being prime by the first 8 Laws of Prime Exclusion.
The first prime factor test we need to try is factoring by 7. Since 91 is a
factored by 7 and 13, the number is not prime.
Addendum Fibonacci
Number Sequence I am including a chart that shows how the famous Fibonacci
Number Sequence has a similar algorithm to the Prime Mod 90 Chart. The hidden
algorithm within the Fibonacci sequence repeats every 24^{th} number.
This is the same number in which the Prime Mod 90 Chart algorithm repeats. I
find it interesting how these hidden algorithms both share the number 24 in
their length.
