OFFSET
1,1
COMMENTS
Let M(n) denote the number of primes p <= n, for which 2^p-1 is prime. It is conjectured that M(n) -> infinity and that M(n) ~ exp(gamma)/log(2)*log(n).
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 1.5 Euler-Mascheroni Constant, p. 29.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
Eric Weisstein's MathWorld, Mersenne Prime
EXAMPLE
2.569544344898573607370044111939...
MATHEMATICA
RealDigits[Exp[EulerGamma]/Log[2], 10, 103] // First
PROG
(PARI) default(realprecision, 100); exp(Euler)/log(2) \\ G. C. Greubel, Sep 06 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Exp(EulerGamma(R))/Log(2); // G. C. Greubel, Sep 06 2018
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Jun 24 2014
STATUS
approved