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%I #20 Mar 13 2023 07:19:23
%S 11,29,83,127,6563,24391,59051,161053,357913,571789,1442899,4782971,
%T 5177719,14348909,18191449,30080233,73560061,80062993,118370773,
%U 127263529,131872231,318611989,344472103
%N Primes q of form q=p^w+2 where p is odd prime, w>=2.
%C For even w, p=3 is the only prime for which p^w+2 can be prime because all primes greater than 3 have the form 6k+-1. For odd w, only primes p=3 and p=6k-1 need to be considered because all primes of the form p=6k+1 will produce a number p^w+2 that is divisible by 3. - _T. D. Noe_, Feb 25 2011
%H T. D. Noe, <a href="/A053703/b053703.txt">Table of n, a(n) for n = 1..1005</a>
%F Primes of A025475(n)+2 form, excluding 1+2.
%F a(n) = A053702(n)+2. [_R. J. Mathar_, Apr 18, 2010]
%e 11=3^2+2, 127=5^3+2, 83=3^4+2, 161051=11^5+2,.. 318611989=683^2+2, 344472103=701^3+2
%t lst={}; Do[p=Prime[n]; fi=FactorInteger[p-2]; If[Length[fi]==1 && Last[Last[fi]]>1, AppendTo[lst,p]], {n,20000000}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Feb 25 2011 *)
%t nn=10^9; t=Table[Select[Table[2 + Prime[i]^k, {i, PrimePi[nn^(1/k)]}], PrimeQ], {k, 2, Log[3, nn]}]; Union[Flatten[t]] (* _T. D. Noe_, Feb 25 2011 *)
%Y Cf. A025475.
%K nonn
%O 1,1
%A _Labos Elemer_, Feb 14 2000
%E Constraint on w added to definition. a(11) appended by _R. J. Mathar_, Apr 18 2010
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