A109799 Primes p such that 2^p - 1 is a Chen prime.

2, 3, 5, 7, 13, 17, 19, 31, 61, 127

Offset: 1

Author

Jason Earls, Aug 15 2005

Keywords

• hard
• more
• nonn

Comments

For p in this sequence, 2^p - 1 is called a Mersenne-Chen prime.

Conjecture: 2^127 - 1 is the largest Mersenne-Chen prime.

Except for the initial term 2, this sequence is the intersection of A000043 and A000978 given by A107360. - Max Alekseyev, Oct 28 2008, Jan 28 2010

Examples

			a(5)=13 because 2^13 - 1 = 8191 is prime and 2^13 + 1 = 3*2731 is semiprime.
		

Crossrefs

Cf. A000043, A000978, A107360, A109611.

Programs

Mathematica

Select[Prime[Range[40]],PrimeQ[2^#-1]&&PrimeOmega[2^#+1]<3&] (* James C. McMahon, Mar 30 2024 *)