OFFSET
1,1
COMMENTS
The last digit of each of these prime numbers is 7.
Subsequence of A078946.
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[171000]], And@@PrimeQ[{#+2, #+6, #+12, #+14, #+20}]&] (* Harvey P. Dale, Jul 23 2011 *)
Select[Prime[Range[171000]], AllTrue[#+{2, 6, 12, 14, 20}, PrimeQ]&] (* or *) Select[ Partition[Prime[Range[171000]], 6, 1], Differences[#]=={2, 4, 6, 2, 6}&][[All, 1]] (* Harvey P. Dale, Sep 04 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Feb 03 2010
STATUS
approved