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Old 2020-03-27, 09:48   #24
gd_barnes's Avatar
May 2007
Kansas; USA

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Originally Posted by LaurV View Post
Sorry for waking up this old thread, but I didn't want to create a new one, and the subject of the current one seems suitable for my silly question:

Why 81 was chosen as the conjectured k for Riesel base 1024?

Because it is the lowest k that has a known covering set of numeric factors for R1024. A factor of 5 covers even-n and a factor of 41 covers odd-n.

Smaller k's k==(1 mod 3, 1 mod 11, & 1 mod 31) have a single trivial factor that eliminates them or others (k=9 & 36) need algebraic factors to eliminate them from consideration.

k=29 does not have a known covering set and is not eliminated by one of the conditions above so we believe it will eventually have a prime. But like many other bases that is just a conjecture at this point. :-)

Last fiddled with by gd_barnes on 2020-03-27 at 09:51
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