A066082 Prime octets: numbers k such that 210*k - 105 +- 2^j are prime for all 1 <= j <= 4.

242590, 1175444, 2416288, 2583146, 2596049, 2796151, 4953911, 5574794, 6127655, 6396209, 6460877, 6625438, 8521234, 11025856, 11352491, 15482298, 16228703, 18861024, 19048003, 20043534, 22835193, 31519781, 34399756

Offset: 1

Author

Frank Ellermann, Dec 03 2001

Keywords

• nonn

Examples

			a(1)=242590 because 210*a(1) - 105 = 50943795 and 50943795 -2, - 4, - 8, - 16, + 2, + 4, + 8 and + 16 are all prime.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..100

Crossrefs

A proper subset of A061671 (prime sextets). Cf. prime quadruples A014561. See also A066081.

Programs

Mathematica

With[{c=2^Range[4]},Select[Range[35*10^6],AllTrue[Flatten[210#-105+ {c,-c}], PrimeQ]&]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jun 10 2015 *)

PARI

{ n=0; for (m=1, 10^12, b=210*m - 105; c=0; for (j=1, 4, if (isprime(b - 2^j) , c++, break)); if (c<4, next); for (j=1, 4, if (isprime(b + 2^j) , c++, break)); if (c == 8, write("b066082.txt", n++, " ", m); if (n==100, return)) ) } \\ Harry J. Smith, Nov 11 2009

Extensions

More terms from Don Reble, Dec 07 2001