[Xiaomi Redmi 4 Prime ROMs, Kernels, Recoveries, & ] Charloam:
That's really interesting, thanks for posting that.

I restored the MIUI global rom where fingerprint is working and did some testing.

cat /proc/kmsg

# what happens when I just unlock the device with the fingerprint sensor
<4>[ 1512.772993] gf:enter irq gf_irq
<4>[ 1512.773857] gf:gf_ioctl, entry
<6>[ 1512.773873] Doesn't support control clock.
<4>[ 1512.773885] gf:gf_ioctl, exit
<4>[ 1512.790203] gf:gf_ioctl, entry
<4>[ 1512.790238] gf:gf_ioctl, exit
<4>[ 1512.986288] gf:gf_ioctl, entry
[B]<3>[ 1512.986320] goodix_fp soc:goodix_fp: Selected 'goodixfp_reset_reset'
<3>[ 1512.989333] goodix_fp soc:goodix_fp: Selected 'goodixfp_reset_active'
<6>[ 1512.989342] goodix_fp soc:goodix_fp: IRQ after reset 1[/B]
<4>[ 1512.992349] gf:gf_ioctl, exit
<4>[ 1513.004349] gf:gf_ioctl, entry
<4>[ 1513.004436] gf:gf_ioctl, exit
<4>[ 1513.004439] gf:enter irq gf_irq
<4>[ 1513.054765] gf:gf_ioctl, entry
<4>[ 1513.054783] IRQ has been enabled.
<4>[ 1513.054788] gf:gf_ioctl, exit
<4>[ 1513.055288] gf:gf_ioctl, entry
<3>[ 1513.055327] goodix_fp soc:goodix_fp: Selected 'goodixfp_reset_reset'
<4>[ 1513.055369] gf:enter irq gf_irq
<3>[ 1513.058379] goodix_fp soc:goodix_fp: Selected 'goodixfp_reset_active'
<6>[ 1513.058410] goodix_fp soc:goodix_fp: IRQ after reset 1
<4>[ 1513.061421] gf:gf_ioctl, exit
<4>[ 1513.061533] gf:gf_ioctl, entry
<4>[ 1513.061539] IRQ has been enabled.
<4>[ 1513.061544] gf:gf_ioctl, exit
<4>[ 1513.070007] gf:gf_ioctl, entry
<6>[ 1513.070017] Doesn't support control clock.
<4>[ 1513.070112] gf:gf_ioctl, exit

# what happens when I unlock the device with the button (as a sort of control)
<4>[ 1319.890174] gf:gf_ioctl, entry
<4>[ 1319.890195] IRQ has been enabled.
<4>[ 1319.890200] gf:gf_ioctl, exit
<4>[ 1319.890611] gf:gf_ioctl, entry
<6>[ 1319.890627] Doesn't support control clock.
<4>[ 1319.890632] gf:gf_ioctl, exit
<4>[ 1319.890684] gf:gf_ioctl, entry
<3>[ 1319.890714] goodix_fp soc:goodix_fp: Selected 'goodixfp_reset_reset'
<4>[ 1319.890752] gf:enter irq gf_irq
<3>[ 1319.893740] goodix_fp soc:goodix_fp: Selected 'goodixfp_reset_active'
<6>[ 1319.893756] goodix_fp soc:goodix_fp: IRQ after reset 1
<4>[ 1319.896763] gf:gf_ioctl, exit
<4>[ 1319.896852] gf:gf_ioctl, entry
<4>[ 1319.896861] IRQ has been enabled.
<4>[ 1319.896866] gf:gf_ioctl, exit
<4>[ 1319.906359] gf:gf_ioctl, entry
<6>[ 1319.906376] Doesn't support control clock.
<4>[ 1319.906381] gf:gf_ioctl, exit

AIDA64 output (of questionable reliability from what I've read elsewhere)
############
Fingerprint Scanner
Manufacturer FPC / Goodix
Model FPC102x / FP

Also, referencing your link, it seems that a method to tell if you have FPC or Goodix was to try to take a phone in MIUI camera by pressing the fingerprint sensor. If it works then you have FPC. Mine doesn't, although it's a different device. Another check was looking for goodix/fpc in /sys/class/input/input?/name, but none of them reference either.

Goodix sensors were the sensors not supported by CM also, so I think I have a Goodix sensor, but I'm not certain.

Could anyone else do any testing to check which sensor they have on their R4P?

EDIT: Doing a bugreport I find:

[ro.boot.fpsensor]: [gdx]

Pretty convinced I have a goodix fingerprint sensor at this point. Can anyone else find out if their Redmi 4 Prime has a Goodix/FPC sensor?