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A218046
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Primes p such that 8p + 2r is a primorial for some r in A006512.
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2
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2, 11, 23, 83, 113, 131, 173, 191, 233, 239, 251, 263, 281, 293, 359, 419, 431, 449, 503, 641, 653, 659, 701, 719, 743, 761, 809, 821, 881, 911, 953, 1013, 1019, 1031, 1049, 1103, 1223, 1229, 1289, 1301, 1433, 1439, 1451, 1493, 1511, 1559, 1583, 1601, 1619
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OFFSET
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1,1
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COMMENTS
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The primes p in this sequence satisfy b#/2 = 4p + r, where p is a prime, b# is a primorial, and r is the second of the twin prime pair (r-2, r).
Each p is therefore associated with at least one primorial, and with a pair of twin primes.
The empirical evidence suggests that each twin prime pair is associated with at least one p, and each p with a twin prime pair. I conjecture that this sequence (and therefore the sequence of twin primes) is infinite.
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LINKS
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Charles R Greathouse IV, Table of n, a(n) for n = 1..354
Michael Kaarhus, Twin Prime Conjectures 1, 2 and 3, 2012, (PDF)
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EXAMPLE
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8*2 + 2*7 = 5#
8*11 + 2*61 = 7#
8*23 + 2*13 = 7#
8*83 + 2*823 = 11#
8*113 + 2*14563 = 13#
8*131 + 2*254731 = 17#
8*173 + 2*463 = 11#
8*191 + 2*14251 = 13#
8*233 + 2*14083 = 13#
8*239 + 2*199 = 11#
8*251 + 2*151 = 11#
8*263 + 2*103 = 11#
8*281 + 2*31 = 11#
8*293 + 2*307444891294244533 = 47#
8*359 + 2*253819 = 17#
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PROG
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(PARI) list(lim)={
my(v=List(), P=3, q);
forprime(p=5, lim,
P*=p;
forprime(t=2, min(lim, (P-2)\4),
q=P-4*t;
if(q%6==1 && ispseudoprime(q) && ispseudoprime(q-2), listput(v, t))
)
);
vecsort(Vec(v), , 8)
}; \\ Charles R Greathouse IV, Oct 23 2012
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CROSSREFS
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Sequence in context: A338225 A106974 A198277 * A342185 A217309 A115374
Adjacent sequences: A218043 A218044 A218045 * A218047 A218048 A218049
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KEYWORD
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nonn
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AUTHOR
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Michael G. Kaarhus, Oct 19 2012
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EXTENSIONS
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Terms corrected by Charles R Greathouse IV, Oct 23 2012
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STATUS
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approved
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