**Prime Numbers** fit a pattern of graphically predictable *“Vertical Prime Pairs”* of Primes and SemiPrimes [Prime1 x Prime2] in these Digital Tables:

The numerical values are arranged by

*vertical*Leading Digit**x 10**

**+***horizontal*Last Digit.

The pattern repeats every 30 numbers and even though the *positions* of the pairs are clearly NOT random, the values and distribution of primes and semiprimes appear not to be predictable.

Thus we see the fundamental *digital *differences between:

*multiplication*which involves two*factors**addition*which uses two*summands*- and
*counting*which adds 1 and*decimal*Orders of Magnitude [10^{0}, 10^{1}, 10^{2}…]

Furthermore, these screenshots display the *sorting *of Prime Numbers by their Last Digits. And they show the difference between **PRIME Digits** **2** **3** **5** **7** and **LAST Digits 1 3 7 9**. They have **3** and **7** in common, whereas the differences are **2** and **5 **vs **1** and **9**:

- LAST Digits act as
**potential Prime “indicators**“;

- PRIME Digits are of
**arithmetic**and**dimensional**significance:-**1**and**9**:- as Last Digits they are 10 ± 1 as a basis for additions and subtractions;
- additions and subtractions are
*linear*and*bi-directional*or**1D**operations;

**2**and**5**:- as Factors
**2 x 5**and**5 x 2**they form*vertical*and*horizontal*rectangles as ‘decimal units’,*geometrically*speaking; - multiplication is
*square*or*rectangular*as**2D**operation.

- as Factors

Below 10:

- Prime Digits
**2**and**5**form**2 x 5 = 10**, i.e. they lay the foundation for 2D “*decimal*rectangles“,*geometrically*speaking.

Above 10:

- Last Digits
**1**and**9 = 10 ± 1**, i.e. they surround multiples of 10 along the 1D Number Line.

When Prime Numbers become ‘Prime *Factors’* to produce SemiPrimes, we see these tables:

**Why on earth **could these *series *be important in this *pattern*? Let me count the reasons:

- in terms of
*education*and the difference between*belief*vs*knowledge,*Plato’s analogy of the Cave tells us that we need to distinguish between:- what is in our
*mind*from the use of words as*concepts* - and what is before our
*eyes*from the use of images as*perceptions;*

- what is in our
- the general assumption is that there is no pattern, and thus no
*predictability*or*formula*for Prime Numbers;- these “Digital Table” patterns predict the presence of “Vertical Pairs” of Primes (sums) and SemiPrimes (products) in specific cell positions;
- this means a digital or ‘holy mix’ between sums and products;

- equally ‘difficult’ is the Factorisation of SemiPrimes described as the ‘hardest’ on this Wikipedia page on Integer factorisation;
- yet ‘deep’ and ‘spreadsheet-enabled’ thinking made it possible for me;

- in my manual work
**the pattern was always right!**- this meant I could predict the next product of primes for the empty fields in the pattern of “Diagonally Staggered Prime Pairs”:
- the pattern tells me which
*number*it will be; - I just had to find its
*factors;*

- the pattern tells me which

- this meant I could predict the next product of primes for the empty fields in the pattern of “Diagonally Staggered Prime Pairs”:
- I wrote a
*Factorisation Table*built on the sequence**6n ± 1**which I picked up from Dr Peter Plichta in an article he published in the German magazine Spektrum in the 90s;- more recently, I created six screenshots as Collection 9 on The Factorisation of SemiPrimes;

*products*advance faster than*sums;*- the ‘primality’ test of whether a number is prime or not is thus always lagging behind the SemiPrimes whose prime factors are known;
- if we turn them into a LookUp Table, Bob’s our uncle!

*spreadsheets*allow me to cut and paste much larger matrices and tables – often one cell at a time – and, again,**the pattern is always right!**- the primes are unpredictable ‘givens’;
- SemiPrimes are ‘predictable fillers’ – most intriguingly made up from these unpredictable prime numbers;
- the predictability of SemiPrimes is shown in a Functional Matrix:
- i.e. the multiplication of
*vertical*with*horizontal*Primes below the diagonal - or
*horizontal*Primes x*vertical*Primes for SemiPrimes*symmetrically*above the diagonal.

- i.e. the multiplication of

It depends entirely on ‘prior knowledge’ or bias and preconceived ideas whether and how this website will make a difference. I’ve just tried my best to be as clear as possible.