20061027, 14:31  #67  
Nov 2003
2^{2}·5·373 Posts 
Quote:
IT IS NOT AN INTEGER. Basic Calculus. Would someone please get rid of this crank? 

20061027, 15:41  #68  
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}×3^{3}×19 Posts 
First Principles
Quote:
With all the criticisms directed to you, Troels, I know I am throwing a straw to a drowning man. So please dont use off the cuff statements without testing them out, either this, or face ridicule. From First Principles. In these and subsequent posts in this thread I’m taking on the role of Marin Mersenne, who kept topics of maths alive between several math’cians and their theories, in an open correspondence with one and all. As such the maths presented here are not mine but those of Troels Munkner from his book ‘A Prime number Theorem’. Kindly address all queries , valuable hints, criticism to him and not to me. Troels, allow me to take relevant extracts from the above mentioned book and condense them systematically, as Your book is not as coherent as it should be. I hope you will clarify many questions that may be raised so that your theory may be fully and significantly discussed and analysed, and further developed. All posters and partakers kindly treat this as a GIMPS project to get a better knowledge of Primes and perhaps an appropriate and faster algorithm than what is in use, and I say Perhaps ! Munkner starts with the classification of integers in his opening chapter. 1) The Integers: All integers have been subdivided into two sets of numbers called (1) ‘Never primes’ (NP) and (2) Possible primes (PP) 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. PP can be subdivided into real primes and Prime Products (P’P’) PP constitute 1/3 of all numbers. PP constitute a multiplicative system which becomes ‘skew’ because of the off set of one in the regularity of factors. It is not easy to find the prime factors except when the number is a square number, you substitute the PP by 1 x the (Number in question). Munkner goes on to give a graphical display of this series by sine curves. Even Integers: 2. sin (pi.N/2) Never Primes: divisible by 3 as 6 sin (pi.N/6 + pi/2) . For possible Primes 5 , 7 , 11 and 13 … 30. sin (pi.N./30 + pi/6 ) ; 42 sin ( pi. N/42 – pi/6) 66.sin (pi.N/66 + pi/6) ; 78. sin (pi.N/78 – pi/6 ) Then he gives a composite graphical display of all the curves His next chapter will be on Prime products and I reserve this for another post .I welcome your comments and analysis and refrain from my own. Mally 

20061027, 15:50  #69 
Aug 2002
2^{3}×1,051 Posts 
Throwing a straw? What is a drowning man going to do with a straw?
along with alone caseztuchz in ni to express everything out of fo r those the is impossible! inpossible ing ion outy uoty withy wihty iny niy outhy uothy outh uoth 
20061027, 15:59  #70  
Bronze Medalist
Jan 2004
Mumbai,India
804_{16} Posts 
A Straw.
Quote:
It means I am not of much help but I offer hope. Mally 

20061027, 16:00  #71 
∂^{2}ω=0
Sep 2002
República de California
11·1,063 Posts 

20061027, 18:09  #72 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
6336_{10} Posts 

20061027, 18:09  #73 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
2×3×1,709 Posts 

20061027, 18:27  #74 
∂^{2}ω=0
Sep 2002
República de California
11×1,063 Posts 
Oh, it's forum bug (or, thankfully, now exforum bug) alright, but not in the way you're thinking. I think Xyzzy is just having a bit of fun using the peculiar syntactical style of that nowbanned Raman666 nutter who started that massive GMP_ECM thread (more of a personal insanity blog, actually) on the Factoring forum. Actually, it *would* be kinda cool to have a feature that would allow one to Ramanize selected posts  but I asked Xyzzy about an analogous piglatinizing feature last April 1st, and he said it was a nogo, so if you want your posts to look "special" this way, you ottagay oday itay ourselfyay.
Last fiddled with by ewmayer on 20061027 at 18:28 
20061029, 12:37  #75  
Aug 2005
Brazil
2×181 Posts 
Quote:


20061029, 15:24  #76  
Bronze Medalist
Jan 2004
Mumbai,India
100000000100_{2} Posts 
Possible prime.
Quote:
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. Mally 

20061031, 17:38  #77 
Oct 2006
7 Posts 
Paterns of primes, part 2
Well, background always seems trivial.
A prime number is always a prime number. If prime numbers of a specified size can only end in certain digits in a given base, than they can not end in any other digit in that base. Therefore, if a number when expressed as a multidigit number in some base does not end in a digit available for multidigit prime numbers in that base, then it is not prime. Every base has its own set of digits of which a multidigit prime must end. For example: Base six multidigit primes must end in 1 or 5 Base ten multidigit primes must end in 1, 3, 7, or 9 Base twelve multidigit primes must end in (digit equivelents of) 1, 5, 7, or 11 Base fifteen multidigit primes must end in (digit equivelents of) 1, 2, 4, 7, 8, 11, 13, or 14 Base thirty multidigit primes must end in (digit equivelents of) 1, 7, 11, 13, 17, 19, 23, or 29 Base two hundred ten multidigit primes must end in (digit equivelents of) 1, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 143, 149, 151, 157, 163, 167, 169, 173, 179, 181, 187, 191, 193, 197, 199, or 209. Look at these as paterns or cycles. Of the six listed above six, ten, fifteen, thirty, and two huindred ten are distinct from each other. As far as spacing of prime numbers is concerned the cycle for base twelve is two repeations of the cycle for base six. Consider these cycles the way we treat other waveforms. They can behave similarly to constructive and destructive interference. A prime number would occur whenever the cycles for all bases, less than the number, positively reinforce. If any base, where a number is multidigit, it ends in a not available digit (for example 12 in base thirty, which would be a multiple of six.) than that number is not prime. 
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