Please refer to the blog "HP Prime not detected on PC".
Below is the solution from the above post:
Did it download the latest firmware files onto your computer? You can check this by opening your <Documents>/HP Connectivity Kit/Firmware directory. Do you see files in there? If not, try to manually download the files and unzip them into that directory. Here is the link to the zip file:http://ftp.hp.com/pub/calculators/Prime/HP_Prime_Calculator_Firmware_20160829.zip(this is the latest at the moment I write this message)
Third, unplug your calculator. If it is in that "recovery mode" you mention - great! That is the mode we want it in. If not, please do this procedure: Hold down the SYMB key, and while SYMB is still held down, click the ON button. The calculator will drop into the "recovery mode" as long as you kept holding the SYMB button down.
Lastly, connect your calculator (use a different USB port if you have one then where you were first connected). Open the windows connkit, and the calculator should run the update.
What is happening here is this: when the calculator switches into that "recovery" mode, Windows is not registering that the usb is now in update mode and so it doesn't load the driver needed. Thus the connkit can't talk to it. This problem was corrected, but your calculator is old enough it doesn't have that fix in there yet. Hence why I directed you to unplug first, put it into recovery mode, and connect to a different usb plug. One of those steps should trigger it to load the correct driver.
I'am an HP Employee
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