AP's 200th book of science// Primes are ILL defined in Mathematics // Math focus by Archimedes Plutonium

[Archimedes Plutonium]

AP's 200th book of science// Primes are ILL defined in Mathematics // Math focus by Archimedes Plutonium.

A shame that Galois invented Groups, Ring,Field over the nonsense of quintic. But by 1830 in math history, it was not known that a Well Defined Equation of math had to have a positive nonzero number to the rightside of the equation at all times, and never be zero. Because the moment you do that, there never arises a problem of quintic.

And what Galois should have done with his time, was reason that groups rings and fields need to be invented for the purpose of a WELL DEFINED OPERATOR in mathematics.

It should not be AP that corrects all of Algebra of mathematics, but it should have been Galois or Gauss or Riemann to have done that by 1830.

Prime concept is a hallucination of Old Math. Ask any physicist where does the concept of prime arise in physics? It never does, and the reason being is mathematicians are kooks in defining prime.

Sure, mathematicians have known for centuries that primes have No Pattern, have No Formula. But you would expect at least one marble of brain power from these mathematicians to notice that if No Pattern, No Formula, that something is wrong with the definition of primes.

What is wrong in the definition? It is simple and tells us why primes have no pattern, have no formula-- To be Well Defined Operator, a operator must obey N#M = P where # is the operator (in our case, division) and N,M,P must be Counting Numbers to be well defined. So in other words a Well Defined operator over a set of numbers, must deliver to you when you operate N#M, must deliver to you another Counting Number P. Primes of Old Math only sometimes obeys that axiom of well defined. But immediately we have numbers outside of Counting Numbers such as 1/2, 1/3, 2/3, etc etc.

ILL defined primes is the reason Primes have NO PATTERN, have NO FORMULA, and also, since no pattern, cannot have any Theorems.

The theorem of concern in this post is the Unique Prime Factorization Theorem. It is a sham proof. And it is a sad reflection of the lack of any logical intelligence on the part of 90% of math professors. They all knew primes have no pattern, but not able to put 2 and 2 together to make 4. If you have no pattern, you cannot have a general theorem over primes.

This post is about harnessing the computers of the world to fetch out the first Large Odd Number that has 2 independent sets of prime solutions. Below I give a illustration of a Odd number which has 4 prime factors. It possibly has a 2nd set of prime factors independent of the first that equals the odd number in question when multiplied.

I predict before the year 2022 ends, a computer somewhere on Earth will unearth a large Odd Number that has 2 independent sets of prime factors.

On Tuesday, August 16, 2022 at 6:25:06 PM UTC-5, Archimedes Plutonium wrote:
> On Tuesday, August 16, 2022 at 4:07:37 PM UTC-5, James Waldby wrote:
> > Barry Schwarz <schw...@delq.com> wrote:
> > > On Tue, 9 Aug 2022 11:03:31 -0700 (PDT), "henh...@gmail.com" wrote:
> > > <snip>
> > >> i wonder...
> > >>after 101 (prime), what's the next prime of the form 1000.....001
> > > <snip>
> > >
> > > Numbers of the form 10^N+1 for N = 3 to 125 are all composite. 11 and
> > > 101 appear to be the most frequent factors
> > In much the same way that 2^N + 1 can be prime only when N is a power
> > of two (giving a Fermat prime), for any integer base b > 1 the number
> > b^N + 1 can be prime only when N is a power of two. See ref for
> > simple proof. (Basically, if N is odd b+1 is a factor of b^N + 1; and
> > if N = p*q with p or q odd, b^N + 1 = (b^p)^q + 1; hence N has no odd
> > factors if b^N + 1 is prime; hence N is a power of 2 if b^N + 1 is
> > prime.) Ref: <https://math.stackexchange.com/a/2794244/13324>
> >
> > This python program reports only 11 and 101 among primes of form
> > 1+10^N, for exponents up to N = 2^17 :
> >
> Are primes of form 1000..009 as sparse as 1000..001 ?? The reason I ask is because both the 9 and 1 endings have 3 ways of fetching a composite-- 1x1 = 1 , 3x7 ends in 1 and 9x9 ends in 1. As for 9 ending, 1x9 ends in 9, 3x3 ends in 9 and 7x7 ends in 9.
>
> Can you tell us, if the 1000..009 is as equinumerous in composites as is the 1000..001
>
> Also, more important, can you train your computer to look for a Odd large Number which has 2 sets of Prime factors, each set independent of the other.
>
> For example, some large odd number of 1000..001 which has a set of 3 different primes, and a different set of just 2 primes that equals the odd number. In other words, the Unique Prime Factorization theorem does not hold true in general.
>

So let me give that example again.
The composite number
100,000,000,000,001 = 29 x 101 x 281 x 121499449.

This is a composite with 4 prime factors with a ending of 9x9 to equal the 1 ending in 10^14 +1.

The square root is about 10,000,000. The square root of 10^7 is about 3162.

So, I am looking for primes of about 31620 with that of 10^14 divided by 31620.

Easy for computers, burdensome for AP with hand held calculator.
So, looking at prime number 31627. Now, what I predict is that there is a large Odd Number which say has 4 Known prime factors. But this large odd number has a second set of prime factors independent of the first set. This second set has just 2 prime factors. And those two prime factors are primes and obviously not divisible by any prime in the first set.

If this was a case of what I am looking for, then the factors of 31627 accompanied by a second prime factor must end in a "3" digit in order to retrieve a "1" as the last digit.

This is just an illustration of what is looked for.

Obviously when mathematicians start finding these multiple sets of prime factors, the Old Math theorem of Unique Prime Factorization has to be thrown out the window and onto the trash pile of shame.

And the reason for this is not an extension of prime number theory, no, the reason being is that primes of Old Math are ILL Defined for Counting Numbers have no well defined division operation. To be well defined a operator # must by N#M=P where all three N,M,P reside within Counting Numbers. Just 1/2 or 2/3 violate that rule.

Primes as ILL Defined means never a Pattern to primes, never a Formula for primes, and now we see, never a theorem on primes.

I am predicting that before year 2022 ends, that someone with a good computer will announce they found a Odd large number with 2 independent sets of Prime Factors.

AP

[Archimedes Plutonium]

When people have been brainwashed, it is difficult to instruct and guide them into anything new, that goes against their brainwashing. Math professors were brainwashed to think there is Unique Prime Factorization, although to their credit, they realized there was never a pattern to primes. Yet they had not sufficient marbles of logic to make the further step-- if primes have no pattern, surely, no theorem on primes can be true in general. No-one in Old Math was intelligent enough to understand that no pattern, no formula for primes meant the Unique Prime Factorization Theorem was a load of b.s. In that vain I repeat my illustration, to ease the brainwashed mind that some Large Odd Numbers have two different sets of prime factors. But I need computers to find these strange Large Odd numbers.

Archimedes Plutonium
Aug 13, 2022, 12:33:12 AM
to Plutonium Atom Universe
Let me give you an example of what I am looking for, but an exacting example, for mine is an illustration.

The odd number 299 = 13 x 23, but what if 299 was equal to a different set of primes 3 x 3 x 3 x 11 (although that is 297).

So, what I am looking for is a composite number that has two different sets of prime multiplications. And finding such a composite number destroys Old Math algebra with its ILL defined concept of prime numbers.

AP

[Archimedes Plutonium]

Nowhere in Physics or Chemistry, is the concept of "prime of mathematics" ever needed, ever used. The concepts of even and odd are found throughout physics and chemistry, but never is the concept of prime come up, even once. It simply is nonexistent in science except for kooks of mathematics.

AP replaces the numbers of mathematics with the Decimal Grid System of Numbers, and they do not have a concept of prime.

See AP's TEACHING TRUE MATHEMATICS series of textbooks.

AP