I don't think any current LLM is a Turing machine or Turing complete.  LLMs are programs, so they lack the physical components of a Turing machine all together, and they have some differences which prevent them from simulating one. Turing machines read and write data in order to perform operations. As a result, they can perform any algorithm (provided they're given enough time and infinite read/write space). LLMs are generative, so they mimic the structures of text they have been trained on. The structure of current LLMs results in a phenomenon known as *halucination*, or "just making things up", which means that any attempt to simulate a Turing machine may be convincing, but pushing it far enough will reveal it to be a false one. The LLM will loose track of data, a conversation's direction, etc.
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