Marcus, Some more comments on your collaboration with Claude.
A Russian team Robert Gerbicz, Leonid Durman, Yuri Radaev, and Alexey Zubkov implemented a C++ brute force search up to d < 2 * 10^9. They use 2^10 as the main reduction rather than 5^4 as you and I did. I have also invented a different type of brute force search on a/8, b/8 instead of on d, c. For my elliptic curve research, I have been using sage which includes a cythonized PARI/GP package. I have also found pari's ellrank and hyperellratpoints to be the most efficient tools. I have seen patterns in the known solutions that lead me to suspect that modular forms can be used to bridge from a known elliptic curve fiber to a new one or from a hyperelliptic quartic to a new one. But I have not yet found any useful methods. Feel free to turn your agents loose on my GitHub repository where all of this is documented: https://github.com/rfryeSigma/Euler_413. In particular, check out the two tables of known solutions in the code folder: solutions.py, solutions_uv.csv . These tables include the 13 solutions < 10^27 and also solution 19 in your table 2. Solutions 14-18 are easily derived from these tables, but not documented. -Roger > On May 18, 2026, at 6:08 AM, Roger Frye <[email protected]> wrote: > > Marcus, > Thank you. Very interesting research. > I haven’t found anything False or anything new in it yet, but I will continue > studying the .pdf. > The research misses the recent work by Tito Piezas III, which has proved most > productive. > This could be remedied quickly by including math.stackexchange in your search > corpus. > -Roger > >> On May 17, 2026, at 6:46 PM, Marcus Daniels <[email protected]> wrote: >> >> Here’s some new work by Opus 4.7 with MCP tooling from me. >> <session_writeup_v9.pdf>.- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / >> .-- .-. --- -. --. / ... --- -- . / .- .-. . / ..- ... . ..-. ..- .-.. >> FRIAM Applied Complexity Group listserv >> Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom >> https://bit.ly/virtualfriam >> to (un)subscribe http://redfish.com/mailman/listinfo/friam_redfish.com >> FRIAM-COMIC http://friam-comic.blogspot.com/ >> archives: 5/2017 thru present >> https://redfish.com/pipermail/friam_redfish.com/ >> 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/ > >
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