Eberhart's Conjecture
If 
is the 
th prime such that 
is a Mersenne Prime, then
It was modified by Wagstaff (1983) to yield
where
is the Euler-Mascheroni Constant.
References
Ribenboim, P. The Book of Prime Number Records, 2nd ed. New York: Springer-Verlag, pp. 332-333, 1989. Wagstaff, S. S. ``Divisors of Mersenne Numbers.'' Math. Comput. 40, 385-397, 1983.
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