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 A172456 Primes p such that (p, p+2, p+6, p+12, p+14, p+20) is a prime sextuple. 3
 17, 1277, 1607, 3527, 4637, 71327, 97367, 113147, 191447, 290657, 312197, 416387, 418337, 421697, 450797, 566537, 795647, 886967, 922067, 1090877, 1179317, 1300127, 1464257, 1632467, 1749257, 1866857, 1901357, 2073347, 2322107 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The last digit of each of these prime numbers is 7. Subsequence of A078946. The primes do not have to be consecutive. - Harvey P. Dale, Jul 23 2011 The primes are always consecutive: The few ways of inserting other primes are: (p,p+2,p+4)... [impossible since one of these would be a multiple of 3]; (p,p+2,p+6),(p+8),(p+12),(p+14) [impossible since one of these would be a multiple of 5]; (p,p+2,p+6),(p+10) [impossible since one of these would be a multiple of 3]; (p,p+2,p+6),(p+12),(p+14),(p+16) [impossible since one of these would be a multiple of 3]; (p,p+2,p+6),(p+12),(p+14),(p+18) [impossible since one of these would be a multiple of 5]. - R. J. Mathar, Jun 15 2013 REFERENCES R. K. Guy, Unsolved Problems in Number Theory, E30. LINKS Amiram Eldar, Table of n, a(n) for n = 1..1000 G. E. Andrews, MacMahon's prime numbers of measurement, Amer. Math. Monthly, 82 (1975), 922-923. T. Forbes, Prime k-tuplets R. L. Graham and C. B. A. Peck, Problem E1910, Amer. Math. Monthly, 75 (1968), 80-81. P. A. MacMahon, The prime numbers of measurement on a scale, Proc. Camb. Phil. Soc. 21 (1923), 651-654; reprinted in Coll. Papers I, pp. 797-800. Eric Weisstein's World of Mathematics, Prime Triplet. EXAMPLE The first two terms correspond to the sextuples (17,19,23,29,31,37) and (1277,1279,1283,1289,1291,1297). MAPLE for n from 1 by 2 to 400000 do; if isprime(n) and isprime(n+2) and isprime(n+6) and isprime(n+12) and isprime(n + 14) and isprime(n+20) then print(n) else fi; od; MATHEMATICA Select[Prime[Range], And@@PrimeQ[{#+2, #+6, #+12, #+14, #+20}]&] (* Harvey P. Dale, Jul 23 2011 *) CROSSREFS Initial members of prime quadruples (p, p+2, p+6, p+12): A172454. Cf. A073648, A098412. Sequence in context: A222985 A229833 A305872 * A022012 A022546 A268067 Adjacent sequences:  A172453 A172454 A172455 * A172457 A172458 A172459 KEYWORD nonn AUTHOR Michel Lagneau, Feb 03 2010 STATUS approved

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Last modified June 18 19:52 EDT 2021. Contains 345120 sequences. (Running on oeis4.)