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Old 2021-03-02, 00:53   #6
Dr Sardonicus
 
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Feb 2017
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It's not entirely clear to me how the double checking of an LL test using a left-shifted initial value is supposed to work. From what I have read,

1) The LL left-shifted double-check is only done when the initial LL test says the number is composite. (If the initial LL test says it's prime, the LL test is repeated by hordes of volunteers using different programs on different types of hardware.)

2) I read one place that the final "double check" residue is "adjusted" after the last iteration, to account for the original left shift of the starting value. Alas, there was no explanation of how this is done.

3) AFAICT the "adjusted" value from the double-check test doesn't actually have to be equal to the value from the original test. The residues only have to agree in the 64 least significant bits.
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