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]> 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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