Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #30 Sep 08 2022 08:45:13
%S 2,7,29,641
%N Primes of form 2^n + 5^n.
%C 2^n+p^n is prime if n=0;or n=1 and p is a smaller of twin primes; or n=2 and 4+p^2 is prime; or n=3 and 8+p^3 is prime etc. Several conditions have to be satisfied to get a modest number of terms...
%C n must be zero or a power of two. Checked n being powers of two through 2^22. Thus a(5) > 10^5800000. Primes of this magnitude are rare (about 1 in 13.4 million), so chance of finding one is remote with today's computer algorithms and speeds. - _Robert Price_, May 02 2013
%e For n=4, p=2^4+5^4=641, so p can be prime even when the exponent is not a prime.
%t Select[Table[2^n+5^n,{n,0,5000}],PrimeQ] (* _Harvey P. Dale_, May 28 2014 *)
%o (Magma) [ a: n in [0..2100] | IsPrime(a) where a is 5^n+2^n]; // _Vincenzo Librandi_, Nov 18 2010
%Y Cf. A094473, A094474, A082101, A094476.
%K nonn,easy
%O 1,1
%A _Labos Elemer_, Jun 01 2004