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Can I run Qwen3-4B-MLX-8bit on an RTX 5060?

Yes

Its published weights (4.15 GB) fit in the 7.20 GB an RTX 5060 can use, with room for ≈ 20K tokens of context.

Full analysis of Qwen3-4B-MLX-8bit Everything that runs on RTX 5060 Get the weights on Hugging Face
hf download Qwen/Qwen3-4B-MLX-8bit

Files and context on RTX 5060

Each file of Qwen3-4B-MLX-8bit (and of GGUF versions the site has analyzed), and how much context fits next to it, with the context cache in 16-bit or 8-bit.

FileSizeOn RTX 5060 Context (16-bit)Context (8-bit)
As published4.15 GBFits20K40K
4-bit (estimate)2.26 GBFits33K40K

Qwen3-4B-MLX-8bit on other hardware

Popular models that run on RTX 5060

Assumes 90% of the card's memory is usable and at least 4K tokens of context for one conversation, with the context cache in 16-bit unless noted. Fits leaves at least 20% of that memory for context; Tight leaves less.