%I #19 Sep 07 2019 13:19:41
%S 89,107,127,139,173,179,229,233,349,421,461,521,557,571,727,863,991,
%T 1019,1051,1069,1433,1459,1627,1747,1831,1877,2081,2083,2591,2837,
%U 3229,3319,3361,3541,3677,3697,3761,3877,4201,4229,4259,4271,4349,4451,4561,4591,5011,5119,5147,5171,5531
%N Primes p such that p^16 + 2^16 is also prime.
%C Primes Q = n^16 + 2^16 only for odd n note: Q is divisible by 97 if n = 97k +- 48, n = 97k +- 50, n = 97k +- 66, n = 97k +- 70, n = 97k +- 78, n = 97k +- 84, n = 97k +- 90, n = 97k +- 92 of course there are similar rules for each prime divisor.
%H Muniru A Asiru, <a href="/A157764/b157764.txt">Table of n, a(n) for n = 1..2915</a>
%e For n=89: 89^16 + 2^16 = 15496731425178936435099327796097 is prime and 89 is prime too.
%e For n=3: 3 is (first odd) prime but 3^16 + 2^16 = 43112257 = 3041*14177 (not prime).
%e For n=85: 85^16 + 2^16 = 7425108623606394726715087956161 is prime too, but 85 is not.
%p select(p->isprime(p) and isprime(p^16+2^16), [$1..10^4]); # _Muniru A Asiru_, Feb 04 2018
%t Select[Prime[Range[800]],PrimeQ[#^16+65536]&] (* _Harvey P. Dale_, Sep 07 2019 *)
%o (PARI) isA157764(n) = isprime(n) && isprime(n^16+65536) \\ _Michael B. Porter_, Dec 17 2009
%o (GAP) Filtered(Filtered([1..10^3],IsPrime),p->IsPrime(p) and IsPrime(p^16+2^16)); # _Muniru A Asiru_, Feb 04 2018
%Y Cf. A062324.
%K nonn
%O 1,1
%A Ulrich Krug (leuchtfeuer37(AT)gmx.de), Mar 06 2009
%E More terms from _Muniru A Asiru_, Feb 05 2018