A082101 Primes of form 2^k + 3^k.

2, 5, 13, 97

Offset: 1

Author

Labos Elemer, Apr 14 2003

Keywords

• nonn

Comments

Next term, if it exists, is > 10^125074. - David Wasserman, Aug 13 2004

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

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

If a(5) exists it is greater than 10^16000000. Probably complete. - Charles R Greathouse IV, Apr 29 2013

Examples

			m=0: 1+1, m=1: 2+3, m=2: 4+9, m=4: 16+81.
		

Crossrefs

Cf. A094474-A094499.

Programs

Mathematica

a={}; Do[If[PrimeQ[p=2^n+3^n], AppendTo[a, p]], {n, 0, 10^3}]; a (* Vladimir Joseph Stephan Orlovsky, Aug 07 2008 *)
Select[Table[2^k+3^k,{k,0,100}],PrimeQ] (* Harvey P. Dale, May 14 2014 *)

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