|
%I #29 Jan 13 2019 19:39:01
%S 2,5,13,97
%N Primes of form 2^k + 3^k.
%C Next term, if it exists, is > 10^125074. - _David Wasserman_, Aug 13 2004
%C Since x+y is a factor of x^m+y^m if m is odd, 2^m+3^m is divisible by 2+3=5 unless m is zero or a power of 2. This is similar to Fermat numbers 1+2^m. - _Michael Somos_, Aug 27 2004
%C Checked k being powers of two through 2^21. Thus a(5) > 10^2000000. Primes of this magnitude are rare (about 1 in 4.6 million), so chance of finding one is remote with today's computer algorithms and speeds. - _Robert Price_, Apr 25 2013
%C If a(5) exists it is greater than 10^16000000. Probably complete. - _Charles R Greathouse IV_, Apr 29 2013
%e m=0: 1+1, m=1: 2+3, m=2: 4+9, m=4: 16+81.
%t a={}; Do[If[PrimeQ[p=2^n+3^n], AppendTo[a, p]], {n, 0, 10^3}]; a (* _Vladimir Joseph Stephan Orlovsky_, Aug 07 2008 *)
%t Select[Table[2^k+3^k,{k,0,100}],PrimeQ] (* _Harvey P. Dale_, May 14 2014 *)
%o (PARI) print1(2);for(n=0,99,if(ispseudoprime(t=2^(2^n)+3^(2^n)),print1(", "t))) \\ _Charles R Greathouse IV_, Jul 19 2011
%Y Cf. A094474-A094499.
%K nonn
%O 1,1
%A _Labos Elemer_, Apr 14 2003
|
