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%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
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