A076047 Primes which are the difference between two successive nontrivial prime powers (A025475).

2, 3, 5, 7, 13, 17, 41, 139, 151, 199, 271, 307, 751, 1217, 3343, 3617, 4001, 4241, 40841, 97169, 117017, 203897, 746153, 123090449, 137542193, 256534591, 21249911167, 88109383889, 112332648583, 85726065193313, 226411321073393

Offset: 1

Author

Zak Seidov and Robert G. Wilson v, Oct 29 2002

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

Cf. A025475, A053810, A075308.

Programs

Mathematica

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]

Extensions

More terms from David Wasserman, Mar 31 2005