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Prime numbers order sequence code broken

"Mathematicians have tried in vain to this day to discover some order in the

sequence of prime numbers, and we have reason to believe that it is a mystery into

which the mind will never penetrate" (Wolfram MathWorld, Havil 2003, p. 163)

How the Prime numbers order sequence code was broken appears in Genesis 9 .

My approach and wish is to make my Prime numbers order sequence code

breaking available to a wide audience, starting with 16 year old pupils via a

PowerPoint presentation and without Mathematical language and symbols they

will not understand. Hence Genesis 9 and the preservation of colour coding in this

document.

As Mathematicians, however, might prefer Matrix Algebra language and symbols,

let the column vector [ 6α + 5 ] be A and the column vector [ 6α + 7 ] be B

All Primes, bar 2 and 3, reside in A and B along with a specific set of Composites,

their Composites cohabitants in A and in B

The Composites cohabitants of the Primes in A and in B can be found via the

following four multiplication combinations

1. Multiply each and every element in A with each and every element in A

2. Multiply each and every element in A with each and every element in B

3. Multiply each and every element in B with each and every element in A

4. Multiply each and every element in B with each and every element in B

The Transpose of a column vector X is a row vector X T with the same elements and

in the same sequence as the column vector X.

1. A*AT

2. A*BT

3. B*AT

4. B*BT

2

A*AT and B*BT end up in B and provide the Composites cohabitants of the Primes

in B A*BT

and B*AT end up in A and provide the Composites cohabitants of the Primes

in A Hence

Primes in A = A minus A*BT and A minus B*AT

Primes in B = B minus A*AT and B minus B*BT

Interesting relationships

A*AT , A*BT

, B*AT and B*BT

have a common building block / matrix

Namely the Times Table (Matrix) we all learn early in life, denoted in here as M,

multiplied by 36

A*AT

= 36*M + 6*[ m = 0 plus consecutive Δm = 10, n = 0 plus consecutive Δn = 5 ]

+ [ m = all 25, n = all 25 ]

A*AT second term - Diagonal is composed of 15 = 3*5 multiples

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A*AT third term - All elements = 25 = 5*5

A*BT = 36*M + 6*[ m = 0 plus consecutive Δm = 12, n - 0 plus consecutive Δn = 5 ]

+ [ m = all 35, n = m ]

A*BT second term - Diagonal is composed of 17 = 1*17 multiples

A*BT third term - All elements = 35 = 5*7

B*AT = 36*M + 6*[ m = 0 plus consecutive Δm = 12, n - 0 plus consecutive Δn = 7 ]

+ [ m = all 35, n = m ]

B*AT second term - Diagonal is composed of 19 = 1*19 multiples

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B*AT third term - All elements = 35 = 7*5

B*BT = 36*M + 6*[ m = 0 plus consecutive Δm = 14, n - 0 plus consecutive Δn = 7 ]

+ [ m = all 49, n = m ]

B*BT second term - Diagonal is composed of 21 = 3*7 multiples

B*BT third term - All elements = 49 = 7*7

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Furthermore using as a starting point A*AT the other three multiplication

combinations can be derived via the following Matrix operations.

A*BT minus A*AT = 12 * [ m= 0, 1, 2, 3 etc, n = m ] plus [ m = all 10 = 2*5, n = m ]

B*AT minus A*BT

= 12 * [ m= n, n = 0, 1, 2, 3 etc ] plus [ m = all 0, n = m ]

B*BT minus B*AT

= 12 * [ m= 0, 1, 2, 3 etc, n = m ] plus [ m = all 14 = 2*7, n = m ]

A*BT

minus A*AT first term

A*BT

minus A*AT second term

B*AT minus A*BT

first term

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B*AT minus A*BT

second term

B*BT minus B*AT

first term

B*BT minus B*AT

second term

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The final outcome of all above is

Constantine Adraktas

Massachusetts Institute of Technology ( M I T )

Suite 5 , 59 South Audley Street

Mayfair , Grosvenor Square

London W1K 2QN , England

Mobile Telephone: 00 - 30 - 6944 - 314 - 309

Email: Constantine.Adraktas@MIT-Partners.eu