A (new) prime theorem.

[Maybeso]

Rde:

If I understand that part of troels "terminology" correctly (which I may not), numbers of the form (6*(+m) - 1) are constructed as -(6*(-m) + 1). Like this:
5 -> 6*(-1) + 1 = -5
11 -> 6*(-2) + 1 = -11
17 -> 6*(-3) + 1 = -17
23 -> 6*(-4) + 1 = -23

This is what he means by using +1 as the centre for primes and prime products. If he chose -1, then 5 = 6*1 - 1, and 7 = 6*(-1) - 1. That is why m is taken from -infinity to +infinity instead of just from 1 to +infinity.
(Does he say anything about m = 0?)

It would perhaps be more clear to use |6*m + 1| to indicate the sign of the prime is ignored. I guess he's trying to maintain a consistant clarity throughout.

[S485122]

Originally Posted by Maybeso

If I understand that part of troels "terminology" correctly (which I may not), numbers of the form (6*(+m) - 1) are constructed as -(6*(-m) + 1).
...
It would perhaps be more clear to use |6*m + 1| to indicate the sign of the prime is ignored. I guess he's trying to maintain a consistant clarity throughout.

I am afraid that Mr Munckner more than once denies this and this is why RDE asked Mr Munckner to respond in person. I am afraid that we will get another unclear and sidestepping answer.

I can not say that I see any constant "clarity" in his writing, alas :-(

[mfgoode]

Originally Posted by Maybeso

Rde:

If I understand that part of troels "terminology" correctly (which I may not), numbers of the form (6*(+m) - 1) are constructed as -(6*(-m) + 1). Like this:
5 -> 6*(-1) + 1 = -5
11 -> 6*(-2) + 1 = -11
17 -> 6*(-3) + 1 = -17
23 -> 6*(-4) + 1 = -23

This is what he means by using +1 as the centre for primes and prime products. If he chose -1, then 5 = 6*1 - 1, and 7 = 6*(-1) - 1. That is why m is taken from -infinity to +infinity instead of just from 1 to +infinity.
(Does he say anything about m = 0?)

It would perhaps be more clear to use |6*m + 1| to indicate the sign of the prime is ignored. I guess he's trying to maintain a consistant clarity throughout.

:surprised

Well maybeso, of all the irrelevant posts and criticisms on this subject, I

think you have taken the trouble to understand troels mathematics and lead us all somehwere.

You have hit the nail on the head this time. Congratulations!

I reiterate troels definition from my post #76

[Quote=troels]
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.QUOTE]
Mally

I note that he is taking three centres for his 'zero'.

The zero centred integers and the +- 1 centred integers.

Zero is very much there but is used for 'Never primes' ( see point 2 of his )

For 'possible primes' +- 1 are used as starting points thus

For positive primes like 5 , 7 , 11 etc. use is made of -1 as the centre using

the formula 6M - 1

For negative primes he uses +1 as the the centre thus getting -5 , -7 , etc.

using the formula 6M + 1 [here m is negative]

Of all the replies, yours makes the most sense and we need you to clarify

further what seems to be anomalies. I am sure that with a little trouble to

study troels posts, and with consistency, these could be ironed out,

resulting in a beautiful theory on primes

So please stay tuned Maybeso and I'm passing the baton on to you but will

check troels theory every now and then.

Mally

[brunoparga]

Troels Munkner's definition of a "possible prime", which includes all the primes he's able to recognise as so, is *not* |6m+1|. It's just 6m+1, which implies 5, 11, 17 and 23 aren't primes, or that he'll contradict himself:

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

Originally Posted by troels munkner

1 is false,
2 is true.

Y.s.
Troels Munkner

That is, he has more than once stated clearly that, according to his "theory", every integer must be either even, or divisible by 3, or a "possible prime" (=6m+1). Perhaps he should add another category, like this: even, 3-divisible, "possible prime" and the-ones-I-cannot-understand-why-people-keep-asking-me-about-them, and those would include the (real) primes == -1 (mod 6).

Bruno

[R.D. Silverman]

Originally Posted by brunoparga

Troels Munkner's definition of a "possible prime", which includes all the primes he's able to recognise as so, is *not* |6m+1|. It's just 6m+1, which implies 5, 11, 17 and 23 aren't primes, or that he'll contradict himself:





That is, he has more than once stated clearly that, according to his "theory", every integer must be either even, or divisible by 3, or a "possible prime" (=6m+1). Perhaps he should add another category, like this: even, 3-divisible, "possible prime" and the-ones-I-cannot-understand-why-people-keep-asking-me-about-them, and those would include the (real) primes == -1 (mod 6).

Bruno

He hasn't even presented a "theory". He has said nothing at all.
He has simply observed that the integers that are 1 mod 6 are closed
under multiplication and that they don't include 2 and 3. Big whoopeee.

[Rde]

Originally Posted by R.D. Silverman

He hasn't even presented a "theory". He has said nothing at all.
He has simply observed that the integers that are 1 mod 6 are closed
under multiplication and that they don't include 2 and 3. Big whoopeee.

I totally agree with you. But up to now, nobady could convince troels about that, so I tried it with a very simple question (Im still waiting for an answer).
According to his definitions, if I understood them correctly, 5, 11, ... arent integers because they dont belong to one of his postulated groups. If they arent integers, they cant be used as values for m in his 6*m+1 formula, so I conclude that also 31 (6*5+1) and 67 (6*11+1) arent integers, what leads to a total chaos.

[mfgoode]

Originally Posted by brunoparga

Troels Munkner's definition of a "possible prime", which includes all the primes he's able to recognise as so, is *not* |6m+1|. It's just 6m+1, which implies 5, 11, 17 and 23 aren't primes, or that he'll contradict himself:

That is, he has more than once stated clearly that, according to his "theory", every integer must be either even, or divisible by 3, or a "possible prime" (=6m+1). Perhaps he should add another category, like this: even, 3-divisible, "possible prime" and the-ones-I-cannot-understand-why-people-keep-asking-me-about-them, and those would include the (real) primes == -1 (mod 6).

Bruno

Bruno, I think you caught him off guard on your simple questions. There is a language problem here.

Iwould say please give the man a chance and help him to develop his theory.
By criticism and sarcasm none of us can get anywhere.

But this is maths history all over again. Math'cians with original theories have received scathing attacks from other math'cians whose main purpose is to block the truth with ridicule and discouragement simply because they didnt or couldnt have the imagination to propound a theory themselves.
I am merely stating a historical fact and do not and will not engage in a controversy on this point.

If the moderator (and I appeal specially to Ernst ewmayer) can sieve out all non mathematical posts and comments in this thread I'm sure we could get a viable thread on prime numbers from not only Troels but other competent math'cians like Maybeso to unravel the skein of Troelsian mathematics.

What is the need of the hour is to have posters to look or scratch below the surface of the oxide and reveal the nugget below. Obviously throwing it back into the river cannot help much.

Bruno, for your benefit I quote below from Troels book.

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. [ For this refer to maybeso's and my posts]

Possible primes can be subdivided into real primes and prime products.

The possible primes constitute one third of all numbers [/QUOTE]

Please note that integers 5 , 7 , 11 etc. fall into this category.

Mally

[Rde]

Thx Mally for your answer. This was my best guess too. But the language of troels is everything but clear, so confusion is programmed. But I still dont see any value in troels thoughts (I may not be the only one...)

[grandpascorpion]

97 posts and counting ...

[brunoparga]

Originally Posted by mfgoode

Bruno, for your benefit I quote below from Troels book.

"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. [ For this refer to maybeso's and my posts]

Possible primes can be subdivided into real primes and prime products.

The possible primes constitute one third of all numbers"

Originally Posted by troels munkner

The expression ((6*M)+1) comprises all primes and prime products,

I'd suggest Troels reading his own book again, he seems to have forgotten some of the "theory".

Bruno

[Terence Schraut]

It should be well-know that each base has a set of digits which multi-digit primes in that base can end. But is it, especially for bases other than ten?

Troels munkner's [(6*m)+1] works as well as it does since 1 is a permissable unit's digit for multi-digit prime numbers in base six. If I proposed [(10*n)+3] would generate series of prime numbers with some non-primes mixed in, would anybody notice that 3 is a permissable unit's digit for multi-digit primes in base ten?

It is irksome that troels munkner still seems to be a celebrity after I have made two postings of trivial background on why and what the limits of his formula.