<html aria-label="message body"><head><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body style="overflow-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;">Marcus,<div><span><br></span><span>Some more comments on your collaboration with Claude. </span><div><span><br></span></div><div><span>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.</span></div><div><span><br></span></div><div><span>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.</span></div><div><span><br></span></div><div><span>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.</span></div><div><span><br></span></div><div><span>Feel free to turn your agents loose on my GitHub repository where all of this is documented: </span><a href="https://github.com/rfryeSigma/Euler_413">https://github.com/rfryeSigma/Euler_413</a>. 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.</div><div><span><br></span></div><div><span>-Roger<br id="lineBreakAtBeginningOfMessage"><br><blockquote type="cite">On May 18, 2026, at 6:08\u202fAM, Roger Frye <frye.roger@gmail.com> wrote:<br><br class="Apple-interchange-newline">Marcus,<br>Thank you. Very interesting research.<br>I haven\u2019t found anything False or anything new in it yet, but I will continue studying the .pdf.<br>The research misses the recent work by Tito Piezas III, which has proved most productive.<br>This could be remedied quickly by including math.stackexchange in your search corpus.<br>-Roger<br id="lineBreakAtBeginningOfMessage"><br><blockquote type="cite">On May 17, 2026, at 6:46\u202fPM, Marcus Daniels <marcus@snoutfarm.com> wrote:<br><br class="Apple-interchange-newline">Here\u2019s some new work by Opus 4.7 with MCP tooling from me.<br><session_writeup_v9.pdf>.- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. / ... --- -- . / .- .-. . / ..- ... . ..-. ..- .-..<br>FRIAM Applied Complexity Group listserv<br>Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom https://bit.ly/virtualfriam<br>to (un)subscribe http://redfish.com/mailman/listinfo/friam_redfish.com<br>FRIAM-COMIC http://friam-comic.blogspot.com/<br>archives: 5/2017 thru present https://redfish.com/pipermail/friam_redfish.com/<br> 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/</blockquote><br><br></blockquote><br></span><div></div></div></div></body></html>