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Primes which are the difference between two successive nontrivial prime powers (A025475).
1

%I #8 Mar 31 2012 13:20:45

%S 2,3,5,7,13,17,41,139,151,199,271,307,751,1217,3343,3617,4001,4241,

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

%U 21249911167,88109383889,112332648583,85726065193313,226411321073393

%N Primes which are the difference between two successive nontrivial prime powers (A025475).

%C I have searched through prime powers up to 2^8532. It is very unlikely that there are any other values between the ones listed here, but no prime has been proved to be absent from this sequence. - _David Wasserman_, Mar 31 2005

%e 3 = 128 - 125 = 2^7 - 5^3; 7 = 16 - 9 = 32768 - 32761; 17 = 49 - 32 = 81 - 64 = 529 - 512; 4241 = 528529 - 524288 = 727^2 - 2^19.

%t pp = Sort[ Flatten[ Table[ Prime[n]^i, {n, 1, PrimePi[ Sqrt[10^16]]}, {i, 1, Log[ Prime[n], 10^16]}]]]; l = Length[pp]; d = Sort[Take[pp, -l + 1] - Take[pp, l - 1]]; a = {}; Do[ If[ PrimeQ[ d[[n]]], a = Append[a, d[[n]]]], {n, 1, l - 1}]; Union[a] a = {}; Do[ If[ PrimeQ[ pp[[n + 1]] - pp[[n]]], a = Append[a, pp[[n + 1]] - pp[[n]]]], {n, 1, Length[pp] - 1}]; Union[a]

%Y Cf. A025475, A053810, A075308.

%K nonn

%O 1,1

%A _Zak Seidov_ and _Robert G. Wilson v_, Oct 29 2002

%E More terms from _David Wasserman_, Mar 31 2005