The double check tasks are made from the information gathered by the first (long) task. I think quantum computing is required to do it in reverse :).

I think you have LLR vs. LLR2 a little mixed up. The same primality calculation is run by both programs. LLR2 adds additional steps so that the work can be verified as correct in a very short amount of time, as well as some error-handling algorithms, while LLR requires a duplicate and matching complete calculation.

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It's not possible, unfortunately.

Here's the LLR2 work flow:

1) Main task: Does normal calculation, and also saves a mathematical "proof of work". When the task is done, both the normal result (the regular residue) and the proof data are sent to the server.

2) The server processes the proof, creating the data necessary for the DC task and the expected "secret residue".

3) The DC task is run on a host (probably not the same hast that ran the main task, but it doesn't matter if it is), and the result (a residue) is sent back to the server.

4) The server compares the residue produced by the DC task to the secret residue it created in step 2. If they match, then the original task was correct.

It's impossible to run the DC task (step 3) without first running step 2, which creates the data for step 3. And it's impossible to run step 2 without the data from step 1.

The Fast DC isn't really a double check in the normal sense. It is not checking for primality like the main task. It's a verification that the main task is correct. You can't run the verification without first getting the data from the main task.

Think of it like grading a test. You can't grade the test until after the student takes the test.
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