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Search: id:A105414
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| A105414 |
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Numbers p(n) such that p(n)+2 and p(n+7)-2 are both prime numbers, where p(n) is the n-th prime. |
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| 17, 71, 149, 191, 431, 521, 821, 1049, 1277, 1289, 1451, 1619, 1667, 1877, 1949, 2027, 2657, 3299, 3329, 3467, 3527, 3539, 3767, 3929, 4271, 4931, 5477, 5849, 6131, 6659, 6701, 6779, 6827, 8537, 8819, 8999, 9419, 9719, 9929, 10037, 10091, 11069, 11117
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Conjecture: There are an infinite number of primes p(n) such that p(n)-2 and p(n+k)-2 are both prime for all k > 1.
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EXAMPLE
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p(8)-2 = 17, p(8+6)-2 = 41, both prime, 17 is in the table.
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MATHEMATICA
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For[n = 1, n < 500, n++, If[PrimeQ[Prime[n] + 2], If[PrimeQ[Prime[n + 7] - 2], Print[Prime[n]]]]] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Feb 07 2006
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PROGRAM
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(PARI) pnpk(n, m, k) = \ both are prime { local(x, l1, l2, v1, v2); for(x=1, n, v1 = prime(x)+ k; v2 = prime(x+m)+k; if(isprime(v1)&isprime(v2), \ print1(x", ") print1(v1", ") ) ) }
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CROSSREFS
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Sequence in context: A043230 A044010 A106921 this_sequence A157910 A141959 A069496
Adjacent sequences: A105411 A105412 A105413 this_sequence A105415 A105416 A105417
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KEYWORD
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nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), May 02 2005
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