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A351171
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Initial members of prime sextuples with the penultimate maximum prime sextuple density.
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1
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5553224066557, 110739468138697, 272998795008337, 340913890116967, 501030218150167, 511298368510327, 521361947518117, 1775421737046817, 3060181644401587, 3890546319127327, 4978842456339457, 15709279772033707, 17208741801909517, 20471668463724337
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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5553224066557 + {0, 4, 6, 10, 12, 16, 420, 424, 426, 430, 432, 436} are all primes and form a "cousin sextuple".
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CROSSREFS
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Cf. A022008 (initial members of prime sextuples).
Cf. A094910 (initial members of two consecutive prime sextuples).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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