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A065044
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Start of the first run of exactly n consecutive primes, none of which are twin primes.
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1
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2, 47, 113, 79, 2273, 1097, 467, 1327, 1163, 353, 5749, 3011, 5297, 10151, 1493, 9467, 887, 673, 13033, 9049, 15373, 8641, 28759, 83737, 13411, 18553, 14633, 44777, 54037, 60271, 59693, 142169, 77719, 61583, 178939, 26267, 122887, 293269
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OFFSET
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1,1
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COMMENTS
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Viggo Brun proved that there exist arbitrarily long sequences of primes which are not twin primes (Ribenboim, page 261).
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REFERENCES
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Paulo Ribenboim, The New Book of Prime Number Records, Springer, 1996.
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LINKS
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FORMULA
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EXAMPLE
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79 is the first prime in a run of four consecutive primes (79, 83, 89, 97), none of which are twin primes, and the next larger and smaller primes are each members of a twin pair, so a(4)=79.
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PROG
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(PARI) nextTwin(t)= { until (isprime(t + 2), t=nextprime(t + 3)); return(t) } { default(primelimit, 4294965247); for (n=1, 100, u=2; until((primepi(u) - primepi(t) - 2) == n, t=u; u=nextTwin(t)); if (n==1, t=-3); write("b065044.txt", n, " ", nextprime(t + 3)) ) } \\ Harry J. Smith, Oct 04 2009
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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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