mersenneforum.org > Math S_N cycles in LL done on composite M(p)
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 2010-12-23, 15:59 #1 tichy   Nov 2010 22×19 Posts 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,
2010-12-23, 16:47   #2
R.D. Silverman

Nov 2003

22·5·373 Posts

Quote:
 Originally Posted by tichy 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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