I remember writing a cyberpunk story as a kid, in which everyone was rocking badass 786s.
The Pentium III does sound like a good chip choice for a retro cyberpunk story. Like they said in “The Matrix”, 1999 was the peak of human civilization.
(586 became Pentium, so 686 would be the Pentium Pro/II microarchitecture.)
I recall as a teen wondering if the 486 was so good, how amazing a 1086 was going to be someday :D
Not just you: the Tom Swift novels reboot in the 1990s had Tom once bragging about "the latest seven-eighty-six processor."