How does it compare to the great script restoration?

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And can the Mersenne prime be used to generate *zk* starks?

To verify them yes.

You generate the proof offchain and you verify it on chain

Those are more specific than the ones in GSR. They are really about making efficient STARK proof verification over a specific prime.

So with the arithmetic Opcode's in GSR, how is the size of the proof comparitavely?

GSR will allow for more MEV than these codes as GSR adds a lot more expressivity