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I registered an account just to reply to your comment. After reading the article in question, I was thinking about my own experience. I too have been working o

I registered an account just to reply to your comment. After reading the article in question, I was thinking about my own experience. I too have been working on prime factorization for the past 6 years in the same fashion that you have and what you just wrote here describe perfectly how I feel about my progress and journey. Which makes me wonder... How many people out there are like us, working on the same problem while feeling the same way? It's like the problem is laughing at you. Baiting you back in with its extreme simplicity. It truly is a mesmerizing problem that you can't help but feel is solvable if only one single Eureka moment is reached. Boy do I want this one solved...

skriticos2 8y ago
Not the same problem, but I have been on and off thinking about infinite/recursive compression and compression of random data. Finding patterns in numbers can be very compelling.
- Retric 8y ago
  I have gone down such rabbit holes before. However, it's easy to demonstrate you can't compress arbitrary unbiased random data without going lossy. For every possible input 0 to X you need to map to a different 'compressed' format. So, if you want to handle every possibility then some of your compressed versions need to be as long if not longer than the original version. That's not a problem if their is some bias in how your generating the data. Just map the more common versions to shorter encoding and you get a useful compression even if sometimes it makes things worse on average their is an improvement. But, with unbiased random data you can't chose which subset is more likely because every version is equally likely. Which is why it does not work.
  - odonnellryan 8y ago
    To be said another way: certainly you can figure out a compression algorithm for any one set of data by being clever and taking your time, but that algorithm will not apply to a general case and would be worthless. If you go about finding patterns in a random string it is unlikely that another random string will have those patterns.
    - mojomark 8y ago
      Concur. Said yet another way, one data sets entropy is another data sets negentropy.
convivialdingo 8y ago
Yeah, I’m not even close!! More like the movie Groundhog Day. So far the journey has been really rewarding though. I’ve recently been focusing my efforts on remainders and decision paths. The most invaluable lessons learned have been my understanding of the complexity of simplicity. I’ve written some insanely complicated, convoluted and frankly weird ass code throughout all this. For example: bignum math libraries, modified Euclidean geometry, imaginary number libs, fractal factoring, Russian peasant multiplication, 3D volumetric fluids to triangle area fitting. Multiple geometric shape fitting libraries, Gallois fields and lots and lots of weird what-if code that popped up in my head. I’d always been good at algorithms, but straightforward head-first attacks of the problem always ends in failure. Now I’ve learned to build analysis, statistics and proofs by necessity. It’s completely changed my mindset on design. (Obviously I studied far my comp-sci than mathematics.) Other than sieving and brute force, I think the only other general solution to be a sort of ‘halving’ problem. The relation between factors and q is essential sum or area. You can subdivide either into n buckets and remainders building a tree of nodes iteratively. At many nodes I have found some interesting patterns. I find nodes after some iterations that sum up to a factor. So now my question is finding the path every time. Anyway, best of luck on your journey and enjoy the ride! Maybe in another few years somebody will finally slay this beast.
- mojomark 8y ago
  Also not the same problem, but I've been doing the same with the Traveling Salesman Problem for about 8 years now. It's a love hate play date every Sunday morning.

skriticos2 8y ago

Not the same problem, but I have been on and off thinking about infinite/recursive compression and compression of random data. Finding patterns in numbers can be very compelling.

Retric 8y ago
I have gone down such rabbit holes before. However, it's easy to demonstrate you can't compress arbitrary unbiased random data without going lossy. For every possible input 0 to X you need to map to a different 'compressed' format. So, if you want to handle every possibility then some of your compressed versions need to be as long if not longer than the original version. That's not a problem if their is some bias in how your generating the data. Just map the more common versions to shorter encoding and you get a useful compression even if sometimes it makes things worse on average their is an improvement. But, with unbiased random data you can't chose which subset is more likely because every version is equally likely. Which is why it does not work.
- odonnellryan 8y ago
  To be said another way: certainly you can figure out a compression algorithm for any one set of data by being clever and taking your time, but that algorithm will not apply to a general case and would be worthless. If you go about finding patterns in a random string it is unlikely that another random string will have those patterns.
  - mojomark 8y ago
    Concur. Said yet another way, one data sets entropy is another data sets negentropy.

convivialdingo 8y ago

Yeah, I’m not even close!! More like the movie Groundhog Day. So far the journey has been really rewarding though. I’ve recently been focusing my efforts on remainders and decision paths. The most invaluable lessons learned have been my understanding of the complexity of simplicity. I’ve written some insanely complicated, convoluted and frankly weird ass code throughout all this. For example: bignum math libraries, modified Euclidean geometry, imaginary number libs, fractal factoring, Russian peasant multiplication, 3D volumetric fluids to triangle area fitting. Multiple geometric shape fitting libraries, Gallois fields and lots and lots of weird what-if code that popped up in my head. I’d always been good at algorithms, but straightforward head-first attacks of the problem always ends in failure. Now I’ve learned to build analysis, statistics and proofs by necessity. It’s completely changed my mindset on design. (Obviously I studied far my comp-sci than mathematics.) Other than sieving and brute force, I think the only other general solution to be a sort of ‘halving’ problem. The relation between factors and q is essential sum or area. You can subdivide either into n buckets and remainders building a tree of nodes iteratively. At many nodes I have found some interesting patterns. I find nodes after some iterations that sum up to a factor. So now my question is finding the path every time. Anyway, best of luck on your journey and enjoy the ride! Maybe in another few years somebody will finally slay this beast.

mojomark 8y ago
Also not the same problem, but I've been doing the same with the Traveling Salesman Problem for about 8 years now. It's a love hate play date every Sunday morning.