By Herb Wiggins, M.D.; Clinical Neurosciences; Discoverer/Creator of the Comparison Process/CP Theory/Model; 14 Mar. 2014

The basic concept which best deals with the primes is that of the Prime

Multiples (Prm’s). Those are clearly exclusive of the Primes, and the

primes are by logical definition excluded from being prime multiples. This

is the case. Thus whenever the Prm’s are generated, and eliminated, we are

logically left with the primes. When the language/terminology is better,

the concepts are better, applied more easily and understood better and

faster. There are great and good consequences to good vocabulary and

terminologies. It’s the basis of most all the professional

vocabularies & languages in nearly Every field.

The method has been tested and works by Dugas and O’Connor to numbers 10

exp.9, & is robust.

The same by Sullivan through 2000. and my work shows the same outcome to

2700, without missing a single Prm when accurately done. & a similar method

taking 5200’s & 5300’s in isolation, that is, starting at about 5300, and

sorting above and below that point by 100 numbers, showed that the method

works, completely, accurately and clearly.

So how does this relate to the gaps in the primes? Because the Prm’s

exclude the numbers which are Not Prime. When the PrM’s are consecutive,

the prime gap is consecutive with the PrM’s. And the patterns are very

clear. Take for instance, the huge first primes gap between 113 & 127. This

pattern is blatant, as well. Add 7 to 113, and subtract 7 from 127. We get

120. Now analyze this by the Prm’s methods. 120 is 10 times 12, an even

dozen, which has the largest number of divisors to that point. Then 24 is a

perfect number, and both 120 &12 are multiples of the perfect numbers, 6

and 24.

Now we take 114, even, divisible by 3’s & ~ Prime. Then 115, -5 ending, not

prime and further, 5 times 23, thus a semi prime. Then 116, even divided by

2, 58, and 29 & 4; then 117, divisible by PrM3’s and 9; then 118, even and

divisible by 2 times 59; then 119,divisible by 7 and 17, again Prm’s. Then

120 and that’s the central magical number, divisible by 2, 3, 4, 5, 6, 8,

10, 12, 15, 20, 30, 60, etc. AND the CENTER of the Prime gap, for sure.

Then we have 121, being 11 squared; & then 122, 56, 2, 28, 4, 7, etc;

then 123 3 divisors, and then 124 with other many factors, an even number,

62, 31, 4, and so forth; then 125 which is 5 cubed!!!. Then 126, again

even, 63, 2, 7, 9, 3, and multiples of same. And last, 127 prime!!! The end

of the gap of primes.

The other clear pattern is that the Prm3’s pairs of 2 consecutive quartets almost always fall within those gaps. Thus those are a major contributor to the gaps, plus the other many Prm’s, too, such as 7, 11, 13, 17, etc. & this has been consistently found many, many times. Esp. below 2500. So the gaps ARE created by the Prm’s being particularly concentrated by the periodicities of the interference reinforcement patterns of the Prm’s, mostly. The prime gaps are thus generated in toto by large numbers of consecutive Prm’s, very clearly. It’s that easy to understand, quite frankly.

This Prm pattern is the pattern of the primes, which is like a cast of a

human face, or a casting system for the bronzes. The cast is the primes.

The face and original forms are the Prm’s, for when they are subtracted, we

get the primes by simple, unlimitedly repeating exclusions.

& the rest of the gaps are the same. There is NO pattern to the primes, but

for the pattern of the Prm’s. and this allows the primes to be sorted out

exactly and by exclusion when the Prm’s are created.

There are many ways of doing Prm creation/generation, efficiently, but the

best heretofore is the Atkins method, altho too many ignored the conversion

of the Entire number line to mod60 and then the laborious conversion back

to Mod10. This means it’s not as efficient as claimed.

However, there is a better way, and that’s simple and straight forward &

neuroscientific understanding. Our brains/minds are acutely attuned to

finding patterns, regularity, periodicities. & when we find those in

complex systems, we build our understandings on the Long Term Memories

those repeating, stable, efficient, Least energy patterns create, which

naturally are reinforced into our Long Term Memory systems in the cortical

columns. & then we use those standards to better understand what’s going on.

& that general method repeats without limits, and without constraints.

There are NO limits to the ways that primes can be sorted out. Using the

Prm’s by the long, most direct way, gives us multiples of multiples which

are very time consuming, 7X7’s, 7X primes, 11X11’s, 11, 13, 17, 19, and so

forth. & then the squares of primes, the cubes, etc. That’s what’s going on,

too.

But the least energy rules of Thermodynamic efficiency state we find the

fastest, best, most complete and which gives the best understanding of how,

in a Gaussian practical sense, “Gauss’ Razor”, we sort the primes.

So, when we realize the vast fact that ALL primes are odd numbers, always

ending in -1, -3, -7, -9, and never -5, -0, or even numbers, we can thus

exclude 60% of the number line quickly & efficiently.

We then sort by starting with the primes, 7, 11, 13, 17, 19, then 21, 23,

27, 29. & ever more efficiently by eliminating the Prm3’s, all of them up

to the square of 7, that is 49. We do NOT need to eliminate any other

Prm’s, but the Prm3’s before 49. Which gives the primes to 50!!! At that

time we begin to eliminate the Prm7’s, which are, 77, & 91. That is

7X7, 7X11, & 7X13. And thus have all primes up to 100. Merely by excluding

the 3 and 7 Prm’s in the first 9 quartets!!!

Then we do the 101, 103, 107, and 109 quartets, finding those are all

primes, as they are clearly not removed by Prm’s, & by a simple method. too.

Then we do 111, which is Prm3, then 113, prime, then 117, which is PrM3,

the pattern emerging of the Prm3’s in this method of quartets; and 10

quartets per 100, a centad, that is. Then 121 11 squared, where the Prm11’s

series starts, and 123, Prm3, already done above, and 127, prime, and 129,

Prm3. & we see the repeating, real patterns of paired Prm3’s being

developed here.

The number line consists of periodicities best described by the Zeta

function. But even that can be simplified down. & this is how it’s done.

For Prime 3’s we see this pattern: the casting out 3’s method here.

Add up the digits, and mark Pm3’s as False, the others as T for True

Primes. We find that the Prm3’s are Always in pairs in a quartet, ONLY.

Thus if we find the one, we know that the other is the 2nd following

number. If it’s -1 & Prm3, then the -7 is Prm3. If it’s -3 as Prm3, then

automatically it’s the -9 as Prm3, too. If there is NO Prm3 pairs Ever

found in the first 2 lines ending in -1, & -3, then there are NO Prm3’s in

that quartet. There is NO alternative to this pattern. It’s final, and a

total pattern, without exception.

That removes by a simple addition ALL of the Prm3’s from the quartets to an

unlimited number, does it not? Far, FAR simpler and less processing than

doing the 3+3+3….. method of the E-sieve. Thus sparing ALL of that. One

to Two simple operations per quartet, at most, one 1/3 of the time, and

thus is massively faster than the E-sieve, which must do 60 more

numbers/100 than this method. that’s the Basic casting out 3’s method using

the quartets. But it’s EVER so easy to make it work faster, too. Using a

simple pattern, actually, the Prm3’s can be removed without even doing more

than one calculation, no matter HOW many digits the number line of quartets

has!!! & then extending that wheel without limit down the number line of

quartets to as far as needed, into the 100’s of digits, if desired. More of

that incredibly simple system, later.

Then we have the fast sorter which is of this form. Take a Prime, p, square

it, say 7 to 49, then double 7, get 14, and double that again to 28. Those

are the Prm7 series. by simple, arithmetic function. No lengthy multiplying

of primes together. None of that, at all. All of those multiples of 7, 11,

13, X 17, etc., are not needed. PLUS the primes 7, 11, 13, and their

squares, and cube and p exp. X, without limits, too.

We find then

49 plus 28

77 plus 14

91 + 28,

119 + 14

133+ 28, etc.

With 11 it’s 121 plus 22

143 + 44

187 + 22, etc.

This proceeds at an average rate of Prm7’s by jumps of 14, alt. with 28,

which is 21, average, with Prm7’s. With 11 it’s jumps of 33, on average, and with 17,

jumps of 34 and 68, clearing over 100 digits with only 3 steps, virtually.

As the primes rise in size, the clearing proceeds ever faster. Without

limits. Contrast that to 3, 3, 3, 3, and 7, 7, 7, 7, and 11, 11, 11. It’s

very fast, not having to mess with Prm3’s either.

We find a few -5 endings but not more than 1% of the Prm7’s, series, and

with each successive Prm# such as 11, 13, 17, 19, etc., the same is true,

and those decrease in number. And this is the method. & it’s robust, but

will over call and find the Prm’s as duplicates in each case as a back up

cross check for the method. So if the computer, or if we use a calculator

makes a mistake, those are real periodicities are not seen and thus the

mistake is quickly seen & correctable. What was thought to be a slow down,

was in fact a checking system, which can create Prm’s very, very much

faster by orders of magnitude if desired.

Essentially this finds the primes, and then we plow those back into the Prm’s series, finding ever more. By the time we get, for instance, to 19 sq., 361, we have 73 primes to plow back into the Prm’s generators. Well enough ahead to get to at least 130K of the number line and all of those primes, too. Thus this prime sorting system feeds the Prm’s by a huge amount and does not ever run out of primes to find the primes. It’s that easy.

It can go even faster this way, when the patterns of the successive but not

first Prm’s are located & removed from the number line. Without limits,

too. This is the most rapid way to create the Prm’s and eliminate them from

the number line, leading to a prime list, which grows and grows without

limits, as we reach each prime squared.

This method is way faster by 3 fold than the E-sieve, and actually advances

faster and faster as the size of the primes are squared and then added to.

Thus it generates quickly the Prm’s and the job is done as fast as possible.

That’s the Wiggins Prime Sieve in its nearly most efficient form. However,

the Prm’s which are duplicated, can also be sieved out by a simple pattern,

thus making the system even faster, if properly coded.

& works without limits, too.

This is what can be discovered with understanding the limitless

capabilities of the brain/mind for seeing patterns, and then more pattern

recognition on top of more patterns. The method can likely be made even

more efficient than this. The Log limit of the E-sieve is thus overwhelmed

and is not efficient, or least energy as this method is, and thus Least

energy methods win once more.

That’s the basic form of the Wiggins Prime Sieve, which is copyrighted and

which will threaten the cyber security of the RSA method, because when the

prime arithmetic factors are known, huge lengths of digits of primes can be

ID’d and then listed, and generated by computer methods at ANY point in the number line, when properly coded with these new methods.

And that’s how it’s done. and it’s neuroscientifically supported and robust

as well. Without limits.

When reviewing the QM equations, which are so complex that they cannot be

solved without huge computer power, we are essentially looking at an

analogous situation with the primes computations. Feynman found ways to

simplify the computations with his diagrams & renormalization. These methods of the Prm’s can

also be applied to the QM wave equation for the higher elements, atoms and

isotopes, & to solve those problems of electron levels and isotopic decay

rates, faster, and faster on existing machines. The way is clear for that,

as well.

The periodicities of the natural world, whether they be the Roche numbers

of the planetary, complex system orbits, or the rest of the complex system

families of events, can now be more rapidly sorted than ever, using these

methods.

& that is the Promised Land of the Undiscovered Country of the Complex

Systems. Genetic systems, protein folding and other such periodicities can

then be solved and result in rapid progress in those problems as well. They

way is now clear to understanding much more completely, the limitless

complex systems in our universe.

And this is the Promised Land of Comparison Processing, which recognizes

Least energy processes, which creates S/F relationships of brain, and the

unlimited methods of CP and LE applications. PLUS within the basic

understanding of Complex Systems, now possible.