A351171 Initial members of prime sextuples with the penultimate maximum prime sextuple density.

5553224066557, 110739468138697, 272998795008337, 340913890116967, 501030218150167, 511298368510327, 521361947518117, 1775421737046817, 3060181644401587, 3890546319127327, 4978842456339457, 15709279772033707, 17208741801909517, 20471668463724337

Offset

1,1

Comments

The maximum sextuple density is the triple sextuple where each member is +0, +210, +420; there is currently only one known example of a triple sextuple. These are the "failed" triples where the members are +0, +420, or more exactly: p + d, d = [0, 4, 6, 10, 12, 16] + 420n, n = 0..1.

The maximum density of prime sextuples is the triple of form p + d, d = [0, 4, 6, 10, 12, 16] + 210n, n = 0..2. The first triple prime sextuple is 50038627250687303646277 (from Waldvogel and Leikauf link). While investigating triple sextuples it becomes apparent of the need for failed, or "cousin" sextuples; i.e., when the middle triple sextuple member is not a sextuple.

Links

Julius Schoen, Table of n, a(n) for n = 1..130

Jörg Waldvogel and Peter Leikauf, Finding Clusters of Primes, II (PDF), Seminar for Applied Mathematics SAM, February 2007, May 2013, April 2015, Sect. 2.3, 5-6.

Example

5553224066557 + {0, 4, 6, 10, 12, 16, 420, 424, 426, 430, 432, 436} are all primes and form a "cousin sextuple".

Crossrefs

Cf. A022008 (initial members of prime sextuples).

Cf. A094910 (initial members of two consecutive prime sextuples).

Sequence in context: A258275 A324206 A204349 * A094910 A378474 A295353

Adjacent sequences: A351168 A351169 A351170 * A351172 A351173 A351174

Keyword

nonn

Author

Julius Schoen, Feb 04 2022

Extensions

First six missing terms added by Julius Schoen, Aug 17 2022

Status

approved