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Old 2004-08-01, 18:20   #3
JuanTutors
 
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"Juan Tutors"
Mar 2004

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Thanks jfollas. I actually didn't know about that "random shift" they do. I don't think I was clear enough when I asked my questions, though...

I meant to ask the questions referring to the test unmodified using other tricks like starting from the 3rd term in the sequence or modifying the start value in a way that just helps to verify that the test was run correctly, etc. From what I understand, this "random shift" is just a trick used to help verify the result, and that this "shift" doesn't usually bring S(1)=4 to one of the valid STARTING values of the sequence (like to S(1) = 10 or the other valid starting values depending on the prime being tested).

If you start the test right from the beginning, from S(1) = 4 or 10 or one of the other valid STARTING values of the sequence, i.e. S(1) but not S(2) or S(3), etc, assuming a perfect computer with infinite and infallible accuracy (or, say, an omnipotent God) can the test ever go into a loop or zero out before the end of the test? Is this even known?

Another (arbitrarily hard) one:

Supposing the test can go into loop or zero out before the end of the test, is it true that the test will do so with any/every valid starting value?
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