Hi folks,
After Lucas Wiman's (re)discovery of the factor of M(M(31)), I made some
comment about M(M(p)), something which of course has been long known to not
always be a prime whenever M(p) is. (M(M(13)) is the first counterexample
and even has a factor found by Keller).
Of course, the sequence that still remains unknown is
2
M(2)=3
M(3)=7
M(7)=127
M(127)=170141183460469231731687303715884105727
M(170141183460469231731687303715884105727)=???
the first five of which are prime and the nature of the last still unknown
(hardly surprising!). I noticed Lucas' search found the factor of
M(M(31)) reasonably quickly, a factor which isn't that large a multiple of
M(31) itself.
I checked Chris Caldwell's pages on this, and Curt Noll's trial-factored
M(M(127)) to 5.10^50, surprisingly low considering the size of M(127)
itself, I noticed many other M(M(p)) as listed in
http://www.garlic.com/~wedgingt/MMPstats.txt have only been tested to very
low limits indeed.
I wondered why there wasn't more work done on these - though I understand
it's very hard to motivate people when Guy's law of small numbers no doubt
applies, but everything M(M(61)) and above is currently unknown. It would be
nice to see a few more results there.
Chris
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