"Eureka" was first previewed in the first episode of
Diary of a Surgical Resident: Madoka on January 14, 2025, before
Speedstar Records released the song as a single for download and streaming on Hoshino's 44th birthday: January 28. The song's release was promoted with a teaser—a ten-second video clip posted to social media the morning before the premiere of
Surgical Resident: Madoka, which featured the text "Gen Hoshino Eureka", played over by what
Sports Bull writers called the
percussive sound of
maracas. The single's cover art, photographed by and designed by Hiromi Fujita, depicts Hoshino covered by sunlight as he stares towards the sky. A
phone wallpaper and messaging app
stickers based on the artwork were awarded to users who pre-saved the song on streaming platforms. A promotional photo of Hoshino—also handled by Kawashima and Fujita—was unveiled alongside the song's announcement, and would later be used as the cover art for Hoshino's sixth
studio album,
Gen (2025). "Eureka" is the last single released for the album, on which it is the sixteenth and closing track. Kawashima directed and filmed the "Eureka" music video, which was premiered to
YouTube on January 31, 2025. A behind-the-scenes video, directed and filmed by Koe Inc.'s Yosuke Yamaguchi, was released on March 5, 2025. Hoshino first performed "Eureka" for a two-hour special of
CDTV Live! Live! on February 10, 2025. A minimalistic live version of the song subtitled "808 Sessions"—featuring only Hoshino's soul vocals and digital piano by Hirotaka Sakurada—was uploaded on February 26. It was filmed at Hoshino's home studio 808, where the song and most of the
Gen album were also recorded. Throughout mid-2025, "Eureka" was reprised as the final song before
encore during the Japan leg of
Gen headlining tour, Gen Hoshino Presents Mad Hope. == Reception ==