Originally posted by tuco A film scanner will need a true scan resolution around 3000+ dpi to scan a 35mm film frame at 4k resolution. No commodity scanners scan at that resolution and the ones that do will be expensive. Many scanners advertise much higher resolution but that is interpolated resolution that just enlargers the image and doesn't capture anymore detail.
My CanoScan FS4000US will go to 4,000DPI without interpolation, but that's 20 years old and difficult to find ... it gives something like a 20 megapixel useable scan, nearly 6000x4000 overall, so a scanner with 3,000DPI should go to 4k resolution without problems, but I've not needed to research the marketplace so I've no recommendations.
It's well worth looking for some older s/h hardware, especially if it's only for a one-off job.
The re-sale price, once you're finished with it, is likely to be close to what you paid for it.
Just make sure it's compatible with your operating system and it comes with appropriate drivers/software ... if you need to start licensing third party software, Vuescan for instance, the exercise can get rather more expensive.