How to instantly Identify Prime Numbers

This page of the philosophy of science paper, Time's Paradigm, demonstrates how syncing our decimal system to the Base 4 numerical system pairs primes ad-infinitum.

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Supplement to Time's Paradigm: Prime Numbers Busted


"What is Time? The paradigms and the paradoxes: See Chapter 3.

"An abstract and summary of the chapters can be found on Home Page

"Or, click In a Nutshell, for a condensed overview of arguments.

"Universal Contraction is the core hypothesis of this paper: Read here...

The illusion of progress is as a result of being unable to identify our true position in time and space, as infinity appears to stretch out before us in all directions. Mathematicians created defined points out of necessity, which in turn created paradoxical and unrealistic infinities, as in Zeno's Paradox of motion.

Author: Alan R, Graham

Cyber Security Encryptions:

Understanding prime numbers and how they relate to one another has long been the holy grail of mathematicians - predicting the next one a "Eureka" moment.  Part of the fascination revolves around computers, message encryptions and security systems.  Should someone create a formula to evaluate prime numbers and sub-primes, then servers, mainframes and even the Internet might be severely disrupted around the world.

It is difficult to ascertain whether a very large number might or might not be a Prime Number.  Even more difficult is the task of identifying sub-primes and their divisors.  It can be done, but it takes an awful lot of number crunching in most cases by dedicated high-speed computers.  Mathematicians back in the 60s devised a method of encrypting financial transactions for security reasons:  Secret codes to keep hackers at bay.  They used Prime Numbers and split them to give key numbers to the different parties in communication - for example, a bank liaising with their client.  It is what makes your ATM card secure.  So mathematicians sat back with the comfortable knowledge that Prime Numbers were infallible, as they have with Special Relativity and other corner-stones of our technological empire.

However, there often comes a time when a rock is over-turned, and what is then revealed beneath not always as pleasant nor as trustworthy as one might have hoped.

Mathematicians are hardly at fault for being unable to represent the world around us with any solid reality.  They work with numbers, they create erroneous points with dimensions and infinity paradoxes and then calmly dismiss the obvious, see pt3. Infinity.  So too, do they use a system of decimalization to express the world around us.  But what if our decimal system were flawed, or giving us false impressions?  All mathematical equations are based on the decimal system we first created in the Western World eons ago because, presumably, we have 10 fingers.

The development of the Binary System saw leaps and bounds, not in the world of Prime Numbers but in the speed with which computers and their components can now operate.  Yes or No, was the simplicity behind the Binary System of 0s and 1s.  Perhaps it is time we looked further into numerical base systems and what they can offer.

Prime Numbers Busted:

You will now see below a simple math table amalgamating our decimal system with a Base 4 (Quaternary) system, to reveal the extraordinary fact that every prime number from one to infinity is paired with another, making their identification as we progress upward through the table towards very large numbers, incredibly easy.  Even the special semi-primes are identified.

A Base 4 numerical table that instantly identifies its counterpart primes in the decimal system by pairing with them.  A mathematical breakthrough?  What is going on?  No complicated formulas required, although no doubt some will wish to encapsulate this table with an equation to cross reference prime number identities as the integers rise.  Hence the unnerving thought of a computer capable of extracting all primes and their derivatives in an instant, in the not too distant future.

It is too simple for words.  It seems impossible, but it is true.  Even a child could have drawn this table.  However, more to the point, why is it happening?  Why has it taken mathematicians so long to spot this simple relationship?  What it means for the decimal system could be an early grave.  We have been working for thousands of years with a system that was devised out of the necessity for trading and bartering with fingers, without considering what implications this might have.  Prime Numbers thus surfaced and to this day we see no correlation nor can we interpret their meaning.  Now we can, instantly, using a simple Base 4 Quaternary System.

How to instantly identify any prime number from one to infinity with an incredibly simple Base 4 numerical system.

The numbers on the left of each pair represent our decimal system as they sequentially rise through the table from left to right.  Those numbers paired on the right of the equals signs are Quaternary based, having only 4 sequential integers before continuing in the line above with the next set.

We know that the single digit integers 2, 3, 5 and 7 are Prime Numbers.  From them we see that 5 pairs with 11 and 7 pairs with 13 to identify these new numbers as primes while the table progresses revealing more.  None are missed, every Prime Number is accounted for.

Taking these two new Prime Numbers, 11 and 13 on the Base 4 column, we can then cross-reference them with the decimal column and discover new primes of higher value - 11 now being paired with 23 and 13 with 31.

Though certain Prime Numbers ending in seven or nine, like 17, 47 and 59, may not be identified earlier in the table due to the Quatenary Base 4 system only producing numbers below 4s, they can be identified by using a reduced Base 4 table - that is, a table whose multiple digit numbers do not go beyond the 30s (as one might think should really be the case, anyway).  Example below:

We can now identify 47 as being a Prime Number on the main table because its pair is 113.  Looking at the reduced Base 4 table below, we see that 113 is paired with 23. Following 23 back down the table we see that it is paired with 11, and lower still the Prime Number 5.

0=0  1=1  2=2  3=3

4=10  5=11  6=12  7=13

8=20  9=21  10=22  11=23

12=30  13=31  14=32  15=33

16=100 17=101 18=102 19=103

20=110 21=111 22=112 23=113

24=120 25=121 26=122 27=123

28=130 29=131 30=132 31=133

32=200 33=201 34=202 35=203

36=210 37=211 38=212 39=213

Furthermore, special semi-primes and their derivatives are easily spotted.  For example, 91 is a semi-prime whose claim to fame is that it can only be divided by two lower primes, 7 and 13, both being paired with each other.  Likewise, on the main table, 35 is a super semi-prime of two perfect primes 5 and 7.  35 further up the table identifies a prime number, 83.  There are many ways to cross-reference these tables and their columns to provide answers to a multitude of questions.

But the real question is, WHY?

I have my suspicions, however they will remain as such until I am absolutely certain of my results.

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Time's Paradigm is a philosophy of science paper advocating a Cyclical Time progression. It argues that linear scales like velocity create infinities at both ends, restricting motion, and are necessary mathematical parameters only.

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A synopsis of a work in progress. Copyright: A. Graham, 1988 - 2018

No unauthorised use of the material published or the concepts described herein is permitted.