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

Author

Michel Lagneau, Feb 03 2010

Keywords

• nonn

Comments

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

Examples

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

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.

Crossrefs

Cf. A073648, A098412.

Programs

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 *)

PARI

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