A (new) prime theorem.

[Jens K Andersen]

Originally Posted by Terence Schraut

Every base has its own set of digits of which a multi-digit prime must end.

Your observations about ending digit are trivial and well-known. The explanation:
If a number n ends in digit d when written in base b, then the number has the form n = k*b+d. If a prime p divides both b and d, then p also divides n. This means the only chance of multi-digit primes is when b and d are relatively prime. Dirichlet's theorem says there are infinitely many primes in all such cases. It has also been proved that each d which is relatively prime to n produces the same number of primes asymptotically.

[troels munkner]

Originally Posted by mfgoode

I reiterate Troels definitions.

2) The Never Primes: These comprise all even numbers AND all odd numbers divisible by 3
On the number line NP are located symmetrically around 0 and so may be called 0-centrred integers.
NP constitute 2/3 of all numbers including two real primes No.s 2 and 3.

3) Possible Primes (PP): These are all odd numbers which cannot be divided by 3.
PP are located symmetrically around +1 or – 1 depending on your choice.
These may be called 1-centred integers.
Mally

Dear Malcolm,
Thanks for your replies to other mathematicians and to me.
I have used +1 as the centre for all primes and prime products, and it
has a number of advantages.
The expression ((6*M)+1) comprises all primes and prime products,
M being any or all of the natural numbers from - infinity to + infinity.
((6*(-39)+1) = -233, which´is a prime
((6*(+39)+1) = 235, which is a prime product.

A prime product such as ((6*M)+1) * ((6*N)+1) = 36 (NM) + 6*(M+N) + 1
is an integer, which will never be divisible by 2 or 3. Conclusion: 2 and 3
could be called anything but "primes".

N (just as M) being any or all natural numbers from - infinity to + infinity.
(+) * (+) is of course (+), (-) * (-) will also give a (+) integer,
(+) * (-) will give a (-) integer.
All primes and prime products are divisible by 1 (i.e. N=0).
If you want to look for (M) and (N), which means to factorize a possible
prime, you can do it by subtracting 1 from the integer in question and then
use a second order equation to find or not find the two roots (M) and (N).
If the sum of (M+N) is odd and > 1, the factorization results in
(Even integer)^2 - 3^2 * (an odd integer)^2.
If the sum of (M+N) is 0 or any other even number, the factorization ends in
(Odd integer)^2 - 6^2 * (any integer, including 0)^2.

The sign of a prime or prime product can easily be predicted by modulation
(modulo 9), and it is easy to show if the sum (M+N) is even or odd.

If you have the time you can try to follow my ideas:
7*13 = 91 = 10^2-3^2 etc.
7*19 = 133 = 13^2-6^2 etc.

I am not drowning. I will in fact consider to reflect to the many harsh replies,
which I have received (directly or indirerctly), but maybe it is not worth
the effort. A famous citation from Schiller's Jeanne d'Arc comes to my mind
("-----").

Y.s.
troels

[R.D. Silverman]

Originally Posted by troels munkner

Dear Malcolm,
Thanks for your replies to other mathematicians and to me.
I have used +1 as the centre for all primes and prime products, and it
has a number of advantages.
The expression ((6*M)+1) comprises all primes and prime products,
M being any or all of the natural numbers from - infinity to + infinity.
((6*(-39)+1) = -233, which´is a prime
((6*(+39)+1) = 235, which is a prime product.

A prime product such as ((6*M)+1) * ((6*N)+1) = 36 (NM) + 6*(M+N) + 1
is an integer, which will never be divisible by 2 or 3. Conclusion: 2 and 3
could be called anything but "primes".

<snip>

I must confess to a personal failing.

I do not understandand how people can be so totally clueless as
to spew the kind of nonsense that has been spewed by this troll.

The sad part is that he isn't even aware of how totally clueless
his posts have been.

[Patrick123]

Originally Posted by R.D. Silverman

I must confess to a personal failing.

I do not understandand how people can be so totally clueless as
to spew the kind of nonsense that has been spewed by this troll.

The sad part is that he isn't even aware of how totally clueless
his posts have been.

Chortle, chortle.... snigger, snigger... I hearby declare 6(now named a Monkey Prime) a prime number as no other prime number(according to Munker) is a factor of it

Regards
Patrick

[jasong]

Just as the song goes,"Everybody plays the fool...No exception to the rule..."

EVERYBODY looks stupid at some point, whether they're simply wrong or misunderstood.

I'm not attempting a threat in any way, but I would advise people to not have an overly large amount of fun at Mr. Munkner's expense. As someone who tries to stay in tune with the Holy Spirit, I know that sometimes this stuff can pop up again and give us an unpleasant view of ourselves, something we would rather not aknowledge about ourselves.

As I reread the above, I realize what I said might not even make sense to Christians, so I'll rephrase it: Sometimes when we judge something unfairly, we can suffer for it later on.

[mfgoode]

Originally Posted by troels munkner

Dear Malcolm,
Thanks for your replies to other mathematicians and to me.
I have used +1 as the centre for all primes and prime products, and it
has a number of advantages.

Troels Please clarify this statement. If you put +1 as the centre on the number line does this be like zero on the normal number line? For instance how would you place the prime 7 on this line? Will it be 6 units away from the centre 1 ? or what ?

What most have been confused about is what are the factors of 6.?
We know in real numbers that these are 2 x 3. If you dont include these as prime factors according to your definition, as 2 is an even number and 3 is divisible by 3, and these you call 'never primes', then what would you just call them ?

[QUOTE =Troels} I am not drowning. I will in fact consider to reflect to the many harsh replies,
which I have received (directly or indirerctly), but maybe it is not worth
the effort. A famous citation from Schiller's Jeanne d'Arc comes to my mind
("-----").[/QUOTE]


You have mistaken my sentence which I clarified to Mike also. I have not meant that YOU are a drowning man but I can only offer you as much as a drowning man would feel if I threw him a straw. In simple words ' I cannot offer much help in your theory'.

I will however endeavour to bring out what you mean and put it more coherently for others to understand

Regards

Mally

[troels munkner]

Dear Malcolm,

Thanks for your clarification. The expression ((6*M)+1) comprises all
primes and prime products, M being any natural number from - infinity
to + infinity. But these integers will never be divisible by 2 or 3.

Rather soon you will see some new (and important) threads from me.
I will appreciate your comments.

Y.s.
troels

[troels munkner]

Originally Posted by ewmayer

If that is true, and APNT is basically the same bogus crap you keep posting to this board every few months, it seems their editorial standards are "colossally" low.


You have a most curious definition of "possible prime." Note that I do not intend "curious" to imply in any way that your "definition" is interesting - rather, the kinds of descriptive terms that do come to mind include "idiotic," "clueless", and "wasteful of other people's time." Might I suggest that you either keep your inane musings to yourself, or take them elsewhere? I normally would refrain from using such harsh language, but this is not the first time you've posted this garbage here.


And this tells us what, exactly? That certain perfect squares are ... perfect squares?


So the primes 2 and 3 are in fact not prime, at the same time that any product of your designated 6k+1 possible primes is not clearly composite? You sir, are a moron.


I tremble at the thought of the further "enlightenment" you speak of.

Whoever you are I can predict that you (sooner or later) will regret some of
the replies, which you (directly or indirectly) have sent to me.
From your comments I realize that you have limited knowledge of Latin
and have not looked into a dictionary with translations of foreign phrases.
If you prefer modern, more technical expressions in Esperanto or alike,
the translation of "lapsus calami" will be a "typo".

It is not worthwhile to react to your other replies.

Try to read my threads or replies, open-minded for new ideas.
When you pretty soon will see new threads on "Fermat's small theorem",
"An analysis of (the very few) Mersenne primes and the vast majority of
[2^p -1] products", a new tool "SCET (an acronym for Smallest Common
Exponential Term, radix 2)" and "Riemann's zeta-function" and maybe
want to open these threads, please swallow a couple of tranquillizers before
you make your comments.

Perhaps you can find a translation (in your dictionary) of the following quotation: "Quousque tandem abutere patientia".

Y.s.
troels munkner

[troels munkner]

Originally Posted by ewmayer

If that is true, and APNT is basically the same bogus crap you keep posting to this board every few months, it seems their editorial standards are "colossally" low.


You have a most curious definition of "possible prime." Note that I do not intend "curious" to imply in any way that your "definition" is interesting - rather, the kinds of descriptive terms that do come to mind include "idiotic," "clueless", and "wasteful of other people's time." Might I suggest that you either keep your inane musings to yourself, or take them elsewhere? I normally would refrain from using such harsh language, but this is not the first time you've posted this garbage here.


And this tells us what, exactly? That certain perfect squares are ... perfect squares?


So the primes 2 and 3 are in fact not prime, at the same time that any product of your designated 6k+1 possible primes is not clearly composite? You sir, are a moron.


I tremble at the thought of the further "enlightenment" you speak of.

Whoever you are I can predict that you (sooner or later) will regret some of
the replies, which you (directly or indirectly) have sent to me.
From your comments I realize that you have limited knowledge of Latin
and have not looked into a dictionary with translations of foreign phrases.
If you prefer modern, more technical expressions in Esperanto or alike,
the translation of "lapsus calami" will be a "typo".

It is not worthwhile to react to your other replies.

Try to read my threads or replies, open-minded for new ideas.
When you pretty soon will see new threads on "Fermat's small theorem",
"An analysis of (the very few) Mersenne primes and the vast majority of
[2^p -1] products", a new tool "SCET (an acronym for Smallest Common
Exponential Term, radix 2)" and "Riemann's zeta-function" and maybe
want to open these threads, please swallow a couple of tranquillizers before
you make your comments.

Perhaps you can find a translation (in your dictionary) of the following quotation: "Quousque tandem abutere patientia".

Y.s.
troels munkner

[brunoparga]

It's interesting that Troels criticizes someone else's Latin knowledge and makes such an elementary mistake in the same post.

The correct sentence would be "quousque tandem abutere patientiam". Interestly, it applies perfectly to you, mr. Munkner; how long are you gonna keep coming here, trying to persuade everyone that 2 and 3 aren't prime and that Euclid was a moron?

Bruno

[Rde]

Originally Posted by troels munkner

a polite dialogue will be appreciated
All integers from - infinity to + infinity can be subdivided into three groups.
A. Even integers which will be products of 2 and an other integer.
B. Odd integers divisible by 3 which will be products of 3 and an other
odd integer.
C. Odd integers which are not divisible by 3.
Their general form is (6*m +1), m being an integer from - infinity
to + infinity.

Dear troels

I followed this thread for quite a while now and I always asked myself a very simple question: To which of your three groups do the integer numbers 5, 11, 17, 23, ... belong?

I hope you can enlighten me.