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Old 2010-12-23, 15:59   #1
tichy
 
Nov 2010

7610 Posts
Default S_N cycles in LL done on composite M(p)

Hi,

when LL test is carried out on a composite Mersenne number M(p) then S_N values will start repeating with a certain cycle length, e.g. for p=11 consecutive 60 S_N values will repeat, for p=29 cycle length is 252, and for p=47 it is 20338900. Where do those cycles come from ? (I don't have a degree in mathematics so please excuse my noobness :) )

Thx,
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Old 2010-12-23, 16:47   #2
R.D. Silverman
 
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Nov 2003

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Quote:
Originally Posted by tichy View Post
Hi,

when LL test is carried out on a composite Mersenne number M(p) then S_N values will start repeating with a certain cycle length, e.g. for p=11 consecutive 60 S_N values will repeat, for p=29 cycle length is 252, and for p=47 it is 20338900. Where do those cycles come from ? (I don't have a degree in mathematics so please excuse my noobness :) )

Thx,
Look up "Sylow Theorems". Groups have cyclic sub-groups.
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