A (new) prime theorem.

[Patrick123]

Originally Posted by troels munkner

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

Troels, thank you for your understanding where confusion reigns. I have tried to keep an extremely open mind, I think it was so open that my brains fell out. Besides that, if Dr. Bob Silverman, a man who I can only hope to have a fraction of his knowledge, as well as a number of other learned persons on this forum, query your statements, I seriously wonder who is confused

I shall however, continue to monitor this thread with a chuckle and snort waiting in bated breath for my epithany!

Regards
Patrick

[R.D. Silverman]

Originally Posted by troels munkner

<snip>

I will be patient.....

You have partioned the integers according to their congruence class
mod 6, skipping the class equal to 5 mod 6.

Now what? Do you actually have a theorem to state?

Trivially, the class that is 1 mod 6 is closed under multiplication and
has no member divisible by 2 or 3.

Where do you go from here?

[ewmayer]

Originally Posted by R.D. Silverman

I will be patient.....

I'm starting to get worried about Dr. Silverman ... first he replies politely and with saint-like patience to that insane Raman666 guy that's been stinking up the Factoring forum, now this ... Bob, whatever magic "herb" you recently discovered in your backyard garden - would you consider selling some?

Where do you go from here?

Why, nowhere.

"It's one louder, isn't it?" (Or in this case, "one primer.")

[retina]

Originally Posted by ewmayer

Why, nowhere.

That one link has made this whole thread worthwhile.

[mfgoode]

Originally Posted by ewmayer

I'm starting to get worried about Dr. Silverman ... first he replies politely and with saint-like patience to that insane Raman666 guy that's been stinking up the Factoring forum, now this ... Bob, whatever magic "herb" you recently discovered in your backyard garden - would you consider selling some?

It might be the 'magic' herb Brahmi ( Bacopa monnieri ) well known to the Indian gurus. Nature gives the hint as it is shaped like the brain and also has convolutions resembling it.
Ever wondered how the Chinese discovered Ging Seng ? Well the same way thru Nature.

Originally Posted by

Why, nowhere.

"It's one louder, isn't it?" (Or in this case, "one primer.")

That was good reading Ernst. Must check the vol. control on my sons Fender and amp.

That reminds me I hated, decades ago, the sign outside and inside the London pubs. 'We close at Eleven' which prepared the customers to be ready for work the next morning .

On saturdays and sundays we would have 'elevenses'

http://en.wikipedia.org/wiki/Elevenses

Mally

[ewmayer]

Originally Posted by retina

That one link has made this whole thread worthwhile.

And don't forget to look for our good friend Nigel in one of the recent Volkswagen "V-Dubs Rock" TV Ads:

"This amplifier has airbags ... (falls over backwards with a loud crash) ... I'm OK..."

[troels munkner]

Originally Posted by Wacky

troels,

This statement shows why the reputable mathematicians dismiss your argument.

You choose to exclude "3" based on the above argument. However, at the same time, you choose to include "7", et.al.

Just as you argue about "3", one should make the same argument about "7" (and all other integers).

(By your argument) I must question 7 as a prime. This integer is in fact
a product of 1 (a real prime) and 7 and is not different from ...

Similarly, for 11: This integer is in fact a product of 1 (a real prime) and 11 and is not different from ...

Extending that argument, 1 is the only "prime".

The "problem" with your argument is that it is not self-consistent.
Consistency is a REQUIREMENT of mathematics.

The other point that you seem to miss is that this set of numbers really has little to do with primes. There are more members of the set which are non-primes than there are primes. Therefore, your misuse of the term "prime" is objectionable to many of us. May I suggest that you call these numbers "Munkner Numbers"?

Then you can make statements like the following without raising the ire of mathematicians:

All primes > 3 are Munkner Numbers.

The set of Munkner Numbers is closed under multiplication.

etc.

Whether, or not, you can develop any "interesting" results remains to be seen.


Richard

Dear Richard,
Thanks for your comments.
Let me start with your final suggestion. I don't mind to change terminology
from "possible primes" to "Munkner integers". These expressions cover in fact
the same integers. To use "numbers" instead of "integers" makes no difference, but points to the fact (already mentioned in my publicationn
from 1986) that all "Munkner integers" can be "replaced" by their natural
number M from - infinity to + infinity:--(-7),(-6),(-5),(-4),(-3),(-2),(-1),
0,1,2,3,4,5,6 --, corresponding to (-41),(-35),(-29),(-23),(-17),(-11),(-5),
1,7,13,19,25,31,---
Now I think that you agree to my statement that ((6*M)+1) will never be
divisible by 2 or 3, as (6*M) is divisible by 2 and 3.
Odd integers with modules 0,III or VI (modulo 9) will never be primes
(21 has module III, 51 has module VI, 117 has module 0).
The rest of the odd integers with modules II,V,VIII or I,IV,VII will be
primes or prime products (i.e. "Munkner integers").
Your remark "all primes > 3 are Munkner numbers" should read
"all primes > 3 and all prime products of primes > 3 are Munkner integers".
But you forget the integer 1, which is a product (a square)
of ((6*0)+1) and ((6*0)+1).
You may ask me about the advantages of the terminology "Munkner integers".
They will be evident when I describe the dissection (i.e. the factorization)
of Munkner integers and in addition the dissection of the "Mersenne integers"
which constitute a few primes and a vast majority of prime products.

Y.s. troels

[R.D. Silverman]

Originally Posted by troels munkner

Dear Richard,
Thanks for your comments.
Let me start with your final suggestion. I don't mind to change terminology
from "possible primes" to "Munkner integers". These expressions cover in fact
the same integers. To use "numbers" instead of "integers" makes no difference, but points to the fact (already mentioned in my publicationn
from 1986) that all "Munkner integers" can be "replaced" by their natural
number M from - infinity to + infinity:--(-7),(-6),(-5),(-4),(-3),(-2),(-1),
0,1,2,3,4,5,6 --, corresponding to (-41),(-35),(-29),(-23),(-17),(-11),(-5),
1,7,13,19,25,31,---
Now I think that you agree to my statement that ((6*M)+1) will never be
divisible by 2 or 3, as (6*M) is divisible by 2 and 3.
Odd integers with modules 0,III or VI (modulo 9) will never be primes
(21 has module III, 51 has module VI, 117 has module 0).
The rest of the odd integers with modules II,V,VIII or I,IV,VII will be
primes or prime products (i.e. "Munkner integers").
Your remark "all primes > 3 are Munkner numbers" should read
"all primes > 3 and all prime products of primes > 3 are Munkner integers".
But you forget the integer 1, which is a product (a square)
of ((6*0)+1) and ((6*0)+1).
You may ask me about the advantages of the terminology "Munkner integers".
They will be evident when I describe the dissection (i.e. the factorization)
of Munkner integers and in addition the dissection of the "Mersenne integers"
which constitute a few primes and a vast majority of prime products.

Y.s. troels

(1) Only a crank names a mathematical idea after himself.
(2) You still have not said anything intelligent.

[Mini-Geek]

Originally Posted by R.D. Silverman

(1) Only a crank names a mathematical idea after himself.

Like Mersenne, Fermat, Fibonacci, Sophie Germain, and countless others?

[xilman]

Originally Posted by R.D. Silverman

(1) Only a crank names a mathematical idea after himself.
(2) You still have not said anything intelligent.

To be fair to someone who shows most of the classical signs of being a crank, it was Richard Wackerbarth who wrote: 'May I suggest that you call these numbers "Munkner Numbers"?'

I applaud the change in nomenclature. It greatly reduces opportunities for confusion.

Like you, I'm still waiting for something intelligent to be said.

Paul

[R.D. Silverman]

Originally Posted by Mini-Geek

Like Mersenne, Fermat, Fibonacci, Sophie Germain, and countless others?

These names were assigned by others. The inventors did not name
them after themselves.