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research notes 7.12.2024

I've made significant progress in the inverse karatsuba's method.
result3 acts as test bed for extending the method to all general digital periods past the first.
Results promising. I've moved my research to hard copy.

1. fixed result3 bloat by removing duplication with '[sj, sk]||[sk, sj] not in results3'. Down from ~= 1600 to sub 200 results
2. correct results are now in the list as intended
3. lists not returning empty any more.
4. succeeded in lowering the iteration requirements for the first two digits of n from 1000^2, to 100^2 for generating pairs
5. removed the warmup filtering step where we had to do 10_000**2 for the first two pairs before actually generating results.

Takeaways:
1. The removal of warmup filtering significantly reduced candidate list size on subsequent periods (the 3 digit groups that make up an integer).
2. Correcting the duplicate list entries reduced subsequent period candidates to a rough constant thats sub 200 results for each group. Prior to that the result list grew by roughly 500% for each period.
3. I've been able to demonstrate in code that the specific method for the first three digits of n, for finding the potential first three digits of its factors, are highly likely to extend to all periods of an integer.
4. I've made hardcopies of the new code and research to be distributed.

Todo:
1. Set up a second server rack (mostly junk computers with custom network code) for massive parallel computing on-premise
2. Generalize and extend code to all digital groups or integer periods
3. Implement code that grabs public keys based on domain name
4. Implement code, or dust off prior code in archive, that converts hexadecimal public keys to integers
5. Implement conversion back to hexadecimal
6. Implement code that takes hidden factors of n, once derived, and yields the private key (modulus) of a public key.
7. Rewrite test interface (it's janky) for public use and distribute new work to existing contacts.