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A167771
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Twice-isolated primes: primes p such that neither p+-2 nor p+-4 is prime.
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4
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2, 53, 89, 157, 173, 211, 251, 257, 263, 293, 331, 337, 359, 367, 373, 389, 409, 449, 479, 509, 541, 547, 557, 563, 577, 587, 593, 607, 631, 653, 683, 691, 701, 709, 719, 727, 733, 751, 787, 797, 839, 919, 929, 947, 953, 977, 983, 991, 997, 1039, 1069, 1103
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OFFSET
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1,1
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COMMENTS
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2 together with primes p with property that (p-previous prime)>=6 and (next prime-p)>=6.
By the finitude of the generalized Brun constants, this sequence includes almost all primes.
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LINKS
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EXAMPLE
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a(1)=2 (-2,0,4,6 are nonprimes); a(2)=53 (49,51,55,57 are nonprimes).
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MATHEMATICA
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Join[{2}, Select[Prime[Range[200]], NoneTrue[#+{4, 2, -2, -4}, PrimeQ]&]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 21 2016 *)
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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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STATUS
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approved
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