<<A while back on this list, we had a discussion on just this very thing, but
as it turns out, with some more notable examples, as you have seen, the
deviation, in percent, between so called pairs is pretty far and wide. And
then you have to ask, well, what constitutes a pair anyway? Within 10% of
each other? 20%? Some pairs are ridiculously close when you look at 'em,
and some are pretty far apart but still close enough that some would call it
a pair still. And there's no real correlation to the size of the exponents
either. The deviation grows and shrinks all along the list of primes.>>
Humans are notoriously good at finding patterns in cluttered data. Problem
is, they're also good at finding patterns in random data. This ability is
useful if you're strolling in a field and you see a flash of orange/black.
"Uh oh. Tiger. Run!". It is not useful if you're looking at a shadowed image
of a Mars mountain, or the distribution of Mersenne primes. There seem to be
too many exceptions to the Island theory to make it viable, and islands
aren't observed (to my knowledge) with any other groups of numbers. A while
ago (some people still have this in their archives) I made a trio of
conjectures. <<(#1: That there's a prime around the 4M range that we're
missing. #2: That the discovered M38, which all we knew about was that it was
in the 6M range, was actually around 6.9M, which I was correct about, and #3:
A conjecture about the decamegaprime.)>> The original statement of my
conjecture is buried in a Mersenne Digest < #600, I think. So, to this I add
a fourth conjecture:
#4: The Noll Island Theory is not valid. As more Mersenne primes are
collected, statistical effects due to our small sample size will be lessened.
(I.E. 3 is prime, 5 is prime, 7 is prime, all odd numbers are prime.)
S. "Bonus points to you if you understand my subject and think its funny"
L.</PRE></HTML>
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