> There is a conjecture that the nth Mersenne exponent resulting in a prime
> is approximately (3/2)^n. Consider Mersenne primes through M37. (I don't
> know exactly what M38 is yet, and there may be other small ones.
> Also, the
> double checks of the range through M37 haven't been completed.)
>
> You can see the basis of this conjecture if you use semi-log graph paper
> and graph the index of the Mersenne exponents along the X axis and the
> exponents on the Y axis. If you don't have semi-log graph paper,
> graph the
> log of the exponent. (Or you can use software!) The data is pretty close
> to a straight line.
>
> If you do a linear regression of the log of the exponent vs. the
> index, you
> get a correlation coefficient of 0.996 - which indicates a very strong
> linear relationship. The linear regression parameters yield the relation
> M(n) = 1.4796^n + c, where c is a small constant. 1.4796 is pretty close
> to 3/2.
So, based on this conjecture, what would you guess M38 to be (roughly)?
Should we start a pool to see who can guess the closest to the real
exponent? And those of you who know for sure cannot participate! :-) It'd
be an interesting "experiment" to see just how much this new one fits any
type of pattern.
Aaron
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