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A053703
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Primes q of form q=p^w+2 where p is odd prime, w>=2.
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5
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11, 29, 83, 127, 6563, 24391, 59051, 161053, 357913, 571789, 1442899, 4782971, 5177719, 14348909, 18191449, 30080233, 73560061, 80062993, 118370773, 127263529, 131872231, 318611989, 344472103
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..1005
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FORMULA
| Primes of A025475(n)+2 form, excluding 1+2.
a(n) = A053702(n)+2 [R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 18, 2010]
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EXAMPLE
| 11=3^2+2, 127=5^3+2, 83=3^4+2, 161051=11^5+2,.. 318611989=683^2+2, 344472103=701^3+2
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MATHEMATICA
| lst={}; Do[p=Prime[n]; fi=FactorInteger[p-2]; If[Length[fi]==1 && Last[Last[fi]]>1, AppendTo[lst, p]], {n, 20000000}]; lst (* From Vladimir Joseph Stephan Orlovsky, Feb 25 2011 *)
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 *)
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CROSSREFS
| Cf. A025475.
Sequence in context: A106880 A135064 A179502 * A099911 A118638 A088460
Adjacent sequences: A053700 A053701 A053702 * A053704 A053705 A053706
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Feb 14 2000
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EXTENSIONS
| Constraint on w added to definition. a(11) appended - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 18 2010
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