A (new) prime theorem.

[troels munkner]

Originally Posted by mfgoode

Well jakes, he very generously sent me his book(let) by airmail which he priced at $15 though he has not given me the bill as yet!

I must confess it is even more confusing than his posts. and not well connected from section to chapter.

Never the less, I personally feel,, that he has a message which he cant explain clearly.

Due paucity of time, as Im working on my own theories myself, I have not really studied it.

But if you are interested I could Xerox the booklet and send it to you by post, just for the asking. You may PM me at your leisure.

Regards,

Mally

Dear Malcolm,
The book was a gift.
Sorry that you don't have the necessary time yo read the book.
Please, ask me for additional information, and you will get it.
In the near future I will publish a thread about the structure of Mersenne
primes, which follow exactly the same line as the "possible primes".
It is a pity, that other mathematicians don't have an open mind for
new ideas in this field.

Y.s.

troels

[troels munkner]

Originally Posted by brunoparga

I think the best way to find out what mr. Munkner means would perhaps be asking him plain, simple, easy-to-understand questions.

So, mr. Munkner, please classify both the statements below as either "true" or "false". Whatever your answers are, we've already understood the logic beneath them, so you don't need to spend time explaining why these statements are true or false.

1) The number 5 (positive five) is a prime number. True or false?
2) The number -5 (negative five) is a prime number. True or false?

Please do follow my guidelines strictly, as I personally have a very hard time understanding math which doesn't present itself to me according to them.

Thanks a lot,
Bruno

1 is false,
2 is true.

Y.s.
Troels Munkner

[Patrick123]

Originally Posted by troels munkner

1 is false,
2 is true.

Y.s.
Troels Munkner

I ask you then with tears in my baby blue eyes, if postive 5 is not a prime, then according to your definition, it must be composite. Please tell us the factors or is that a bit more difficult to do than factoring RSA-2048??

Patrick123

[mfgoode]

Originally Posted by Patrick123

I ask you then with tears in my baby blue eyes, if postive 5 is not a prime, then according to your definition, it must be composite. Please tell us the factors or is that a bit more difficult to do than factoring RSA-2048??

Patrick123

Now Pat please dont clout me !

I know you are talking about integers and may I ask which integers?

In Gaussian integers indeed 5 has factors and I mention this as its quite a curiosity which struck my fantasy. Here they are;

(1 + 2i )(1 - 2i ) = + 5 and ( 2i + 1 )(2i - 1 ) = -5

Mally

[ewmayer]

Originally Posted by Patrick123

I ask you then with tears in my baby blue eyes, if postive 5 is not a prime, then according to your definition, it must be composite.

Patrick - it's clear to me that TM is not using "prime" in the normal sense at all. See my post above, where I wrote

Originally Posted by ewmayer

OK, so I'm just going to ignore the silly and confusing "possible primes" verbiage invented by Mr. Munkner, and instead use simply "integers of the form 6*m+1" wherever it occurs.

So when TM says "5 is not prime", just substitute "5 is not of the form 6*m + 1 for integer m", and there you go.

As I also noted, use of misleading/nonstandard/obfuscatory terminology is a hallmark of crankery. If you can't say whatever it is you think you have to say using nonambiguous, easily-understandable standard terminology, that tells me you're either trying to deliberately confuse, or you don't know what you're talking about.

[troels munkner]

Originally Posted by Patrick123

I ask you then with tears in my baby blue eyes, if postive 5 is not a prime, then according to your definition, it must be composite. Please tell us the factors or is that a bit more difficult to do than factoring RSA-2048??

Patrick123

You don't understand my subdivison of integers into three groups:
a) even integers
b) odd integers divisible by 3 (modules 0,III,VI, modulo 9)
c) odd integers with modules V,II,VIII or I,IV,VII.
These integers can be formulated as [(6*m)+1] with m running
from - infinity to + infinity.
[((6*(-1))+1] = - 5
[(6*1) +1] = 7

Possible primes are "located" along a straigt line of integers
(-----,-35,-29,-23,-17,-11,-5, 1,7,13,19,25,31 -----)

Sorry for your tears. I understand that you don't grasp anything.

Y.s.

troels munkner

[mfgoode]

Originally Posted by troels munkner

Dear Malcolm,
The book was a gift.
Sorry that you don't have the necessary time yo read the book.
Please, ask me for additional information, and you will get it.
In the near future I will publish a thread about the structure of Mersenne
primes, which follow exactly the same line as the "possible primes".
It is a pity, that other mathematicians don't have an open mind for
new ideas in this field.

Y.s.

troels

Thank you Troels for the gift. I assure you I will treasure it and when I donate it in my will I hope some math'cian takes it up and completes the theory behind it.

You asked for a proof of the infinitude of primes and you were given Euclid's which is the popular one even in this day

Well there are others which I have but cannot reproduce them due to the complexity of the terms but I will mention their names and you can follow it up from the Book 'The little book of bigger primes' recommended to me by T Rex. and yes it is worth every dollar I paid for it. and the author is Paulo Ribenboim 2nd edition. I'm sure you could locate it in a library near by.

The proofs are by Perrott (1881) Auric (1915), Metrod (1917) and Washington (1980). The last is via commutative algebra.

They have been forgotten and that probably is our fate too in the long run.

Well an Euler or a Gauss turn up every century to redirect the maths path but all cannot claim this honour and neither can they equal them.
So best of luck

Mally

[retina]

Originally Posted by mfgoode

Gaussian integers ... (1 + 2i )(1 - 2i ) = + 5 and ( 2i + 1 )(2i - 1 ) = -5

That can't be it, because according to troels munkner -5 is prime.

[brunoparga]

OK, mr. Munkner, thanks for your answer.

I have another question. You're calling some numbers "prime" and some other "not prime". The former are the ones which fit your 6m+1 formula and the latter are the ones which don't.

My question is, besides fitting the formula above, do primes have any other feature in common? One that fits every prime and no "non-prime"? Please notice that, like my other questions, this one has only two possible answers. The answer must either be "no", or it'll be "yes". If it's "yes" I'd ask you to provide a definition of the common feature of all primes that is as simple, coherent and comprehensive as possible.

Thanks a lot,
Bruno

PS: By common feature I specifically exclude being odd, since that follows from the formula, evidently.

[troels munkner]

Originally Posted by mfgoode

The only reason I can presume to explain this is that 1 is not considered a prime. It is its own square and this property is unique.

Since 2 is considered the only even prime it 'may' also be dropped out of the 'real' prime sequence.

Now Goldbach's conjecture is that every even number greater the two (2=1+1) is the sum of 2 prime numbers. So two is not, by definition above of 1, not being a prime and Goldbach makes 2 an exception to his rule..

Is that what you mean Troels?

But why do you consider 3 as not a prime number? Have you a logical reason?

Mally

Dear Malcolm,
You have kindly submitted three replies with reference to my thread
"A (new) Prime Theorem".
Please recall my definition of "possible primes" [(6*M)+1], M being any
integer from - infinity to + infinity, zero included. M can simply be called
an integer factor (negative, zero or positive).
Let me give you an example with M = - 10 and M = + 10.
The two possible primes will be - 59 and 61 (by modulation V and VII).
The integer [(6*M)+1] will never be divisible by 2 or 3.

All "possible primes" have modules I,IV,VII or V,II,VIII.
All odd integers divisible by 3 have modules = I,III or VI.

I think that you will understand my proposal for a replacement
of the generally accepted (antique) definition of primes.
It is a pity, that many mathematicians don't understand this new idea.

As a consequence of my change of terminology any discussion of
"twin primes" will be of no avail. At the same time Goldbach's conjecture
will be rejected, as it will be incorrect for the sums 4,6,8,10.

Y.s.

Troels Munkner

[victor]

Since the words 'prime' and 'possible prime' already have mathematical definitions, we should not change these definitions. These words also have an historical value...

Mr. Munkner, I suggest you to invent a new set of words applying to your definitions.