A052007 Numbers m such that 2^m + m is prime.

1, 3, 5, 9, 15, 39, 75, 81, 89, 317, 701, 735, 1311, 1881, 3201, 3225, 11795, 88071, 204129, 678561

Offset

1,2

Comments

Terms >= 701 are currently only strong pseudoprimes.

If m=1 (mod 6) or m=2 (mod 6) then 3 divides 2^m+m. Thus for n > 1, a(n)!=1 (mod 6) and a(n)!=2 (mod 6).

Some of the results were computed using the PrimeFormGW (PFGW) primality-testing program. - Hugo Pfoertner, Nov 14 2019

Keller (see Links) notes that a Mersenne number M(2^m+m) = 2^(2^m+m) - 1 can be written as (2^m)*2^(2^m) - 1, and lists the first twelve terms of this sequence. The last known case where M(2^m+m) is prime is for m=a(4)=9, which gives the prime M(521). - Jeppe Stig Nielsen, Apr 20 2021

Links

Table of n, a(n) for n=1..20.

W. Keller, New Cullen Primes, Math. Comp. 64 (1995), 1733-1741, S39.

Henri Lifchitz, Renaud Lifchitz, PRP Top Records. 2^n+n.

Example

2^39 + 39 = 549755813927 is prime.

Mathematica

Do[ If[ PrimeQ[ 2^n + n ], Print[ n ] ], {n, 0, 7000} ]
v={1}; Do[If[Mod[n, 2]*(Mod[n, 6]-1)!= 0&&PrimeQ[2^n+n], v=Append[v, n]; Print[v]], {n, 2, 20000}]

Prog

(PARI) is(n)=isprime(2^n+n) \\ Charles R Greathouse IV, Feb 09 2017

Crossrefs

Cf. A006127, A048744, A129962.

Sequence in context: A217350 A210844 A200148 * A117480 A018260 A334876

Adjacent sequences: A052004 A052005 A052006 * A052008 A052009 A052010

Keyword

nonn,nice,hard,more

Author

G. L. Honaker, Jr. and Patrick De Geest, Nov 15 1999

Extensions

11795 from Farideh Firoozbakht, Aug 21 2003

88071 from Hugo Pfoertner, Dec 26 2004

More terms from Henri Lifchitz submitted by Ray Chandler, Mar 02 2007

Status

approved