A065706 Least member p1 of prime octuplets (p1, p2, p3, ..., p8 = p1 + 26), the eight p's being consecutive primes.

11, 17, 1277, 88793, 113147, 284723, 855713, 1146773, 2580647, 6560993, 15760091, 20737877, 25658441, 58208387, 69156533, 73373537, 74266253, 76170527, 93625991, 100658627, 134764997, 137943347, 165531257, 171958667

Offset

1,1

Comments

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

Links

Harry J. Smith and Dana Jacobsen, Table of n, a(n) for n = 1..18123 [first 100 terms from Harry J. Smith]

Tony Forbes and Norman Luhn, Prime k-tuplets

Norman Luhn, The smallest prime k-tuplets, database of compressed files.

Eric Weisstein's World of Mathematics, k-Tuple Conjecture

Example

a(3) = 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303 = 1277+26 are primes.

Prog

(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

Crossrefs

11 = A065688(8), 26 = A008407(8), 8 = A023193(26+1), octets in A066082 are another (not minimal) constellation of 8 primes.

Union of A022011, A022012 and A022013.

See A257124 (prime septuplets) with an overview of prime k-tuplets.

Sequence in context: A226258 A056705 A259744 * A078874 A257169 A162555

Adjacent sequences: A065703 A065704 A065705 * A065707 A065708 A065709

Keyword

nonn

Author

Frank Ellermann, Dec 05 2001

Status

approved