will this work in HP Prodesk 600 G3 Mini pc?

The Intel Core i5-9600KF Desktop Processor is only compatible with Intel 300 Series Motherboards and requires a discrete GPU. You would need to verify if the HP Prodesk 600 G3 Mini PC has a compatible Intel 300 Series Motherboard and can accommodate the processor's requirements.

Questions & Answers: Intel Core i5-9600KF Desktop Processor i5 9th Gen - Coffee Lake 6-Core 3.7 GHz (4.6 GHz Turbo) LGA 1151 (300 Series) 95W BX80684I59600KF OEM,No Box

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Intel Core i5-9600KF Desktop Processor i5 9th Gen - Coffee Lake 6-Core 3.7 GHz (4.6 GHz Turbo) LGA 1151 (300 Series) 95W BX80684I59600KF OEM,No Box

OEM Processor
9th Gen Intel Processor
Discrete GPU Required - No Integrated Graphics
Only Compatible with Intel 300 Series Motherboard
Socket LGA 1151 (300 Series)
Processor Base Frequency 3.7 GHz
Unlocked Processor
DDR4 Support
Intel Optane Memory and SSD Supported
Cooling device not included - Processor Only
Intel Turbo Boost Technology 2.0 offers powerful productivity, gaming, and overclocking

$93^.50 –