20061108, 00:40  #89 
Aug 2002
Portland, OR USA
2×137 Posts 
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. 
20061108, 07:08  #90  
"Jacob"
Sep 2006
Brussels, Belgium
2^{5}·3·19 Posts 
Quote:
I can not say that I see any constant "clarity" in his writing, alas :( 

20061108, 09:12  #91  
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}×3^{3}×19 Posts 
Troels terminology.
Quote:
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 0centrred 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 1centred 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 

20061108, 15:10  #92  
Feb 2006
Brasília, Brazil
3×71 Posts 
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:
Quote:
Bruno 

20061108, 15:52  #93  
"Bob Silverman"
Nov 2003
North of Boston
2^{3}×3×311 Posts 
Quote:
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. 

20061108, 16:08  #94  
Jan 2006
101010_{2} Posts 
Quote:
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. 

20061108, 17:17  #95  
Bronze Medalist
Jan 2004
Mumbai,India
4004_{8} Posts 
Mistranslation?
Quote:
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 1centred 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 

20061108, 22:25  #96 
Jan 2006
42_{10} Posts 
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...)

20061108, 22:40  #97 
Jan 2005
Transdniestr
503 Posts 
97 posts and counting ...
Last fiddled with by grandpascorpion on 20061108 at 22:40 
20061109, 16:34  #98  
Feb 2006
Brasília, Brazil
3×71 Posts 
Quote:
Quote:
Bruno Last fiddled with by brunoparga on 20061109 at 16:37 Reason: Added Mally's post which shows Troels contradicting his own book 

20061109, 16:48  #99 
Oct 2006
7_{16} Posts 
Troels munkner's theory
It should be wellknow that each base has a set of digits which multidigit 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 multidigit prime numbers in base six. If I proposed [(10*n)+3] would generate series of prime numbers with some nonprimes mixed in, would anybody notice that 3 is a permissable unit's digit for multidigit 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. 
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