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A065706
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Least member p1 of prime octuplets (p1, p2, p3, ..., p8 = p1 + 26), the eight p's being consecutive primes.
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34
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11, 17, 1277, 88793, 113147, 284723, 855713, 1146773, 2580647, 6560993, 15760091, 20737877, 25658441, 58208387, 69156533, 73373537, 74266253, 76170527, 93625991, 100658627, 134764997, 137943347, 165531257, 171958667
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OFFSET
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1,1
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COMMENTS
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3 patterns for 8-tuplets: 11010011001011, 11011010011001 and v.v.
See A022011, A022012 and A022013 for the three different possible patterns. The sequence is conjectured to be infinite, although it is not even proved that there are infinitely many twin primes (p1, p2 = p1+2). - M. F. Hasler, May 02 2015
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LINKS
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EXAMPLE
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a(3) = 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303 = 1277+26 are primes.
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PROG
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(PARI) { n=0; p1=2; p8=19; for (m=1, 10^12, p1=nextprime(p1+1); p8=nextprime(p8+1); if (p8 - p1 == 26, write("b065706.txt", n++, " ", p1); if (n==100, return)) ) } \\ Harry J. Smith, Oct 26 2009
(Perl) use ntheory ":all"; my($s, $e, $i, %h)=(1, 1e10, 0); undef @h{sieve_prime_cluster($s, $e, 2, 6, 8, 12, 18, 20, 26), sieve_prime_cluster($s, $e, 2, 6, 12, 14, 20, 24, 26), sieve_prime_cluster($s, $e, 6, 8, 14, 18, 20, 24, 26)}; say ++$i, " $_" for sort {$a<=>$b} keys %h; # Dana Jacobsen, Oct 10 2015
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CROSSREFS
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See A257124 (prime septuplets) with an overview of prime k-tuplets.
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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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