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
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
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