Luke Welsh writes:
TTBOMK, the theory was never formalized. Regardless, Peter Lawrence
Montgomery settled the issue:
http://www2.netdoor.com/~acurry/mersenne/archive2/0032.html
I assume that the island theory was settled in the negative? I have read the
post, and others. Instead of settling the island theory, it seems that PLM
has supplied an alternative that fits and is well defined.
In http://www.silverlink.net/poke/archive4/0278.html
<http://www.silverlink.net/poke/archive4/0278.html> I summarized the poor
man's predictor - MS Excel trendline of ln(Exponents of Mersenne Primes).
At the time, there were only 36 known Mersenne Primes. The trendline
predicted
p = 1.75(e^(0.4*Ordinal)),
so that trend(M38): p = 6987377.
Updating my spreadsheet to include the actual M36 & M37 gives
p = 1.77(e^(0.4*Ordinal)),
which predicts trend(M38): p = 7067233.
Note, however, that roundoff in the "0.4" multiplier causes a huge change in
the outcome.
When I use the more accurate "0.391", the prediction is p = 5020196.
To me, this trendline seems about as good a fit as PLM's. The range of the
errors is about the same. The range of the squared errors is worse for PLM's
exponential distribution. The error is more centered using the log-linear
trendline.
I don't know enough about the rest, anyone have any comments here?
-Shaun
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