

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
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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), 922923.
T. Forbes, Prime ktuplets
R. L. Graham and C. B. A. Peck, Problem E1910, Amer. Math. Monthly, 75 (1968), 8081.
P. A. MacMahon, The prime numbers of measurement on a scale, Proc. Camb. Phil. Soc. 21 (1923), 651654; reprinted in Coll. Papers I, pp. 797800.
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[171000]], 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



