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A215048
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Number of primes of the form 1 + b^4 for 1 < b < 10^n.
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13
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OFFSET
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1,1
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COMMENTS
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Primes 1 + b^4 are a form of generalized Fermat primes. It is conjectured that a(n) is asymptotic to 0.66974*li(10^n).
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REFERENCES
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Daniel Shanks, On Numbers of the Form n^4 + 1, Math. Comput. 15 (1961), 186-189.
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LINKS
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FORMULA
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EXAMPLE
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a(1) = 3 because the only generalized Fermat primes F_2(b) where b<10^1 are the primes: 17, 257, 1297.
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MATHEMATICA
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Table[Length[Select[Range[2, 10^n-1]^4 + 1, PrimeQ]], {n, 5}] (* T. D. Noe, Aug 02 2012 *)
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PROG
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(PARI) a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^4+1))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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