Without guidance, GPT 5.5 built a multi-threaded MPI code for this and ran it at scale. Reproduced published results in an afternoon.
From: Friam <[email protected]> On Behalf Of Roger Frye Sent: Monday, May 11, 2026 5:20 AM To: The Friday Morning Applied Complexity Coffee Group <[email protected]> Subject: Re: [FRIAM] Why search for more solutions to A^4 + B^4 + C^4 = D^4 ? We chose an arbitrary bound of 10^27 for the size of D because at the time there were less than 100 solutions in that range. (Now we’re up to 109.) When I am looking for relationships between solutions, I extend that to a few thousand < 10^40. If I only look for combinations of 2, we’re up to 10^80 interactions. If I look at a single D^4, I need 10^160. There is more twixt us, Horatio, than atoms. Consider the quantum interactions in a protein molecule. Consider sin(x)/x. A butterfly wherever Carmen SanDiego is. -Roger On May 10, 2026, at 3:16 PM, Frank Wimberly <[email protected]<mailto:[email protected]>> wrote: I read once that there are 10^308 atoms in the visible universe. I'm skeptical. Frank Wimberly 140 Calle Ojo Feliz Santa Fe, NM 87505 505 670-9918 Research: https://www.researchgate.net/profile/Frank_Wimberly2 On Sun, May 10, 2026, 9:53 AM Owen Densmore <[email protected]<mailto:[email protected]>> wrote: Hi Roger, nice to hear from you. Are you still in Santa Fe nowadays? If so, why not drop by Friam at St John's and chat about this? Sounds fascinating! It's interesting that so few numbers we stumble across are really large. And how limited numbers are in computing like in JavaScript, which does have a BigInt but it isn't good for really huge numbers. There is a good library for huge: https://github.com/mikemcl/bignumber.js/. It would be nice if the GPU could handle them. -- Owen On Sat, May 9, 2026 at 8:24 PM Roger Frye <[email protected]<mailto:[email protected]>> wrote: Friends, I just found 2 more today on my birthday. People ask me why I keep searching for more integer solutions to A^4 + B^4 + C^4 = D^4 . Some mathematicians are satisfied to have a proof that there are an infinite number of solutions, not finite, or zero. Statisticians worry about gaps in the distribution known of solutions.There is a suspicious dearth around 10^10 . As a computer jock, I am interested in the algorithms and the bridges between different mathematical formulations. I found a new way to do brute force searching. I’ve refined the two known elliptic curve methods and found a way to use the duality between them. I am searching for isogenies between the elliptic and hyperelliptic curves, but that problem is cryptographically hard. Yet I see patterns that keep me trying. Assistance from AI is laughable at this level of invention. Coding assistants just suggest ways to patch over bugs rather than uncover root causes. Deeper level suggestions for strategy lead down blind alleys almost all the time. I am sure AI will get better, but for now my experience and persistence are winning. -Roger -- still looking for a job. .- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. / ... --- -- . / .- .-. . / ..- ... . ..-. ..- .-.. 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/ .- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. / ... --- -- . / .- .-. . / ..- ... . ..-. ..- .-.. 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/ .- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. / ... --- -- . / .- .-. . / ..- ... . ..-. ..- .-.. 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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