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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
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OFFSET
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1,1
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COMMENTS
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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
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FORMULA
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Primes of A025475(n)+2 form, excluding 1+2.
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EXAMPLE
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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
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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 *)
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
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Constraint on w added to definition. a(11) appended by R. J. Mathar, Apr 18 2010
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STATUS
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approved
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