August 8th, 2016, 06:18 PM  #21 
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 552 
OTheB Number theory is pretty much beyond my knowledge. If the numbers you want to deal with are relatively small, then the coding you want is easily done because each positive number is 1, prime, or a unique product of primes. So if you took the 50 of the 52 letters, both minuscule and majuscule, of the English alphabet, and coded in blocks of three letters, you could use those 50 to code for the first 125000 primes. You would need, I think, to reserve at least one letter for other use. Let's say we reserve Y and Z for other use. So I might code 1 as aab, 2 as aac, 3 as aad, 4 as aacaac, 5 as aae, 6 as aacaad, 7 as aaf, 8 as aacaacaac, 9 as aadaad, and so on. Of course your words would soon become very long, but each would uniquely describe and decompose your number. 
August 8th, 2016, 07:59 PM  #22  
Senior Member Joined: Feb 2016 From: Australia Posts: 1,847 Thanks: 661 Math Focus: Yet to find out.  Quote:
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August 9th, 2016, 03:26 PM  #23 
Newbie Joined: Jan 2016 From: England Posts: 24 Thanks: 0 
This is all very helpful. The aac aad aacaac idea is a lot like what I'm going for, only I would then need to refine this so for instance where 6 would be aacaad, but I'd want to knock it down to size, maybe becoming aabd or caad where it's clear what the two primes are without needing all the information. Minimum information to deduce the components. EDIT: I'll also point out that I won't be using any numbers with more than 3 prime factors or numbers with multiple of the same prime factor. Also the highest prime I'm using is around 1223. 
August 9th, 2016, 08:18 PM  #24  
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 552  Quote:
However, it is obvious that using doubletons of 50 letters (distinguishing between minuscules and majuscules) would let you code 2500 primes directly, which takes you well past 1223. Furthermore, that would leave two doubletons free for other purposes. What seems promising is to reserve one doubleton for 1 and another for a plus sign. You could code many composite numbers up to around 15 billion using between 2 and 3 doubletons, and many primes using between 1 and 4 doubletons. Unfortunately, some numbers starting somewhere around 10000 would result in very cumbersome "words" under the kind of coding scheme I am contemplating. I think you need someone with more knowledge than I have.  
August 10th, 2016, 07:01 AM  #25 
Newbie Joined: Jan 2016 From: England Posts: 24 Thanks: 0 
ok sure, but thanks for the help anyway. I was intending to base it around components of syllables as my system needs restrictions on what letters can follow others. I have 37 onsets (38 at the start of a word), 30 nuclei, and 27 codas. So I have 30,779 word starting syllables and 29,970 other syllables. This again is far more than enough.


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common, factors, numbers, prime 
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