Search - "probably not how it works"
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So I made a couple slight modifications to the formula in the previous post and got some pretty cool results.
The original post is here:
https://devrant.com/rants/5632235/...

The default transformation from p, to the new product (call it p2) leads to *very* large products (even for products of the first 100 primes).

Take for example
a = 6229, b = 10477, p = a*b = 65261233

While the new product the formula generates, has a factor tree that contains our factor (a), the product is huge.

How huge?
6489397687944607231601420206388875594346703505936926682969449167115933666916914363806993605...
and

So huge I put the whole number in a pastebin here:
https://pastebin.com/1bC5kqGH

Now, that number DOES contain our example factor 6229. I demonstrated that in the prior post.
But first, it's huge, 2972 digits long, and second, many of its factors are huge too.

Right from the get go I had hunch, and did (p2 mod p) and the result was surprisingly small, much closer to the original product. Then just to see what happens I subtracted this result from the original product.

The modification looks like this:

(p-(((abs(((((p)-(9**i)-9)+1))-((((9**i)-(p)-9)-2)))-p+1)-p)%p))
The result is '49856916'
Thats within the ballpark of our original product.

And then I factored it.
1, 2, 3, 4, 6, 12, 23, 29, 46, 58, 69, 87, 92, 116, 138, 174, 276, 348, 667, 1334, 2001, 2668, 4002, 6229, 8004, 12458, 18687, 24916, 37374, 74748, 143267, 180641, 286534, 361282, 429801, 541923, 573068, 722564, 859602, 1083846, 1719204, 2167692, 4154743, 8309486, 12464229, 16618972, 24928458, 49856916

Well damn. It's not a-smooth or b-smooth (where 'smoothness' is defined as 'all factors are beneath some number n')
but this is far more approachable than just factoring the original product.

It still requires a value of i equal to
i = floor(a/2)

But the results are actually factorable now if this works for other products.

I rewrote the script and tested on a couple million products and added decimal support, and I'm happy to report it works.
Script is posted here if you want to test it yourself:
https://pastebin.com/RNu1iiQ8

What I'll do next is probably add some basic factorization of trivial primes
(say the first 100), and then figure out the average number of factors in each derived product.

I'm also still working on getting to values of i < a/2, but only having sporadic success.

It also means *very* large numbers (either a subset of them or universally) with *lots* of factors may be reducible to unique products with just two non-trivial factors, but thats a big question mark for now.

@scor if you want to take a look.
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update : we are at hr round baby!!!

part 1 :
https://devrant.com/rants/5528056/...

part 2 (in comments) : https://devrant.com/rants/5550145/...

the tech market is crazy mann! it's one of the top indie fintech companies in our country and has a great valuation.
i totally felt that they i am crashing the interviews , and am seriously not trying to be humble. before the dsa round , i was trying to mug up how insertion sort works 🥲

--------

now my dilemma is should i switch if i get the offer. in a summary:

current company:
- small valuation but profitable (haven't picked funding for last 3 years , so poast valuation is some double digit million \$, but can easily be a unicorn company)
- very major b2b player in my country. almost all unicorns (including this fintech company) and some major MNCs are their client and they have recently acquired a few other companies of us and eu too, making them- a decent global player

- meh work : i love being a cutting edge performer in android but here we make sdks that need to support even legacy banking apps. so tech stack is a lot of verbose java and daily routine includes making very minor changes to actual code and more towards adding tests , maintaining wrapper sdks in react/cordova/unity etc, checking client side code etc.

- awesome work life balance : since work is shit and i am fast enough, i am usually working only 2-4 hours a day. i joined gym, got into shape , and have already vsited 5 places in last 6 months, and i am a guy who didn't used to have time even on sundays. here, we get mote paid leaves than what i would usually need.

- learning opportunities: not exactly from the company codebase, but they provide unlimited access to various course learning platforms like linkedin learning, udemy and others, so i joined some web dev baches and i now know decent frontend too. plus those hybrid sdks also give a light context to new things

new company :
- positives : multi billion valuation, one of the top players in fintech , have been mostly profitable ( except a few quarters)
- positive : b2c so its (hopefully) going to put me back into racing shoes with kotlin, jetpack and latest libraries.
- more \$\$\$ for your boy :)

- negetive : they seem to be on hiring spree and am afraid to junp ship after seeing the recent coinbase layoffs. fintech is scary these days

- negetive : if they are hiring people like me, then then they are probably hiring people worse than me 😂. although thats not my concern what my main concer is how they interviewed. they have hired a 3rd party company that takes interviews of people FOR THEM! i find that extremely impolite, like they don't even wanna spare their devs to hire people they are gonna work with. i find this a toxic, robotic culture and if these are the people in there then i would have a terrible time finding some buddy engineer or some helpful senior.

- negetive : most probably a bad wlb : i worked for an year for a fast paced b2c edtech startup. no matter how old these are , b2c are always shipping new stuff and are therefore hectic. i don't like the boredom here but i would miss the free time to workout :(

so ... any thoughts about it?
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