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Eberhart's Conjecture

If q_n is the nth prime such that M_(q_n) is a Mersenne prime, then

q_n∼(3/2)^n.

It was modified by Wagstaff (1983) to yield Wagstaff's conjecture,

q_n∼(2^(e^(-gamma)))^n,

where gamma is the Euler-Mascheroni constant.

See also

Mersenne Number, Mersenne Prime, Wagstaff's Conjecture

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References

Ribenboim, P. The New Book of Prime Number Records. New York: Springer-Verlag, pp. 412-413, 1996.Slowinski, D. "Searching for the 27th Mersenne Prime." J. Recr. Math. 11, 258-261, 1978/1979.Wagstaff, S. S. "Divisors of Mersenne Numbers." Math. Comput. 40, 385-397, 1983.

Cite this as:

Weisstein, Eric W. "Eberhart's Conjecture." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EberhartsConjecture.html

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