A172454 Primes p such that (p, p+2, p+6, p+12) is a prime quadruple.

5, 11, 17, 41, 101, 227, 347, 641, 1091, 1277, 1427, 1481, 1487, 1607, 2687, 3527, 3917, 4001, 4127, 4637, 4787, 4931, 8231, 9461, 10331, 11777, 12107, 13901, 14627, 16061, 19421, 20747, 21011, 21557, 22271, 23741, 25577, 26681, 26711, 27737

Offset

1,1

Comments

The four primes do not have to be consecutive. - Harvey P. Dale, Jul 23 2011

References

R. K. Guy, Unsolved Problems in Number Theory, E30.

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.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

G. E. Andrews, MacMahon's prime numbers of measurement, Amer. Math. Monthly, 82 (1975), 922-923.

R. L. Graham and C. B. A. Peck, Problem E1910, Amer. Math. Monthly, 75 (1968), 80-81.

Eric Weisstein's World of Mathematics, Prime Triplet.

Example

The first two terms correspond to the quadruples (5,7,11,17) and (11,13,17,23).

Maple

for n from 1 by 2 to 110000 do; if isprime(n) and isprime(n+2) and isprime(n+6) and isprime(n+12) then print(n) else fi; od;

Mathematica

Select[Prime[Range[3100]], And@@PrimeQ[{#+2, #+6, #+12}]&] (* Harvey P. Dale, Jul 23 2011 *)

Prog

(PARI) forprime(p=2, 1e4, if(isprime(p+2)&&isprime(p+6)&&isprime(p+12), print1(p", "))) \\ Charles R Greathouse IV, Mar 04 2012

Crossrefs

Cf. A073648, A098412.

Sequence in context: A341357 A022004 A339503 * A162001 A171713 A375313

Adjacent sequences: A172451 A172452 A172453 * A172455 A172456 A172457

Keyword

nonn

Author

Michel Lagneau, Feb 03 2010

Status

approved