A103901 Mersenne primes p such that M(p) = 2^p - 1 is also a (Mersenne) prime.

3, 7, 31, 127

Offset: 1

Author

Jonathan Sondow, Feb 20 2005

Keywords

• nonn
• more
• hard

Comments

Same as exponents of double Mersenne primes. Only four terms are known.

Examples

			2^2 - 1 = 3 and 2^3 - 1 = 7 are Mersenne primes, so 3 is a member.
		

References

• R. K. Guy, Unsolved Problems in Number Theory, 3rd ed., Springer-Verlag, NY, 2004, Sec. A3.
• G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 3rd ed., Oxford Univ. Press, 1954, p. 16.
• P. Ribenboim, The New Book of Prime Number Records, Springer-Verlag, NY, 1996, Chap. 2, Sec. VII.

Links

• C. K. Caldwell, Mersenne Primes: Conjectures and Unsolved Problems
• Eric Weisstein's World of Mathematics, Double Mersenne Number
• Wikipedia, Mersenne prime

Crossrefs

Cf. A000043, A000668, A001348, A077586, A103902.