login
Primes which occur as the difference of consecutive prime powers >1 as and when they occur.
0

%I #7 Dec 05 2013 19:55:30

%S 7,2,5,17,17,3,41,13,151,17,307,199,139,271,1217,7,751,3617,4241,3343,

%T 4001,97169,40841,117017,746153,203897,137542193,256534591,123090449

%N Primes which occur as the difference of consecutive prime powers >1 as and when they occur.

%C Conjecture: Every prime is a member.

%C These are the prime terms of A053707 in the order that they are found. Odd primes will be found only when one of the consecutive powers is a power of 2.

%e 41 is a member with 41 = 13^2- 2^7.

%t t = {}; Do[If[! PrimeQ[n] && PrimePowerQ[n], AppendTo[t, n]], {n, 3000000}]; Select[Differences[t], PrimeQ] (* _Jayanta Basu_, Jul 04 2013 *)

%Y Cf. A076047, A077273

%K nonn

%O 1,1

%A _Amarnath Murthy_, Aug 10 2002

%E Corrected, extended, and edited by _T. D. Noe_, Apr 12 2009