A138660 Primes p such that (12*p - 1, 12*p + 1) and (18*p - 1, 18*p + 1) are twin primes.

29, 1051, 6719, 9059, 10501, 27749, 27791, 36749, 51421, 83761, 86729, 108751, 115249, 120049, 124139, 124529, 138629, 148861, 152839, 162091, 169009, 176609, 178249, 178921, 202481, 203141, 209621, 228199, 232681, 244411, 302779, 309259

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, May 15 2008

Keywords

• nonn

Examples

			29 is a term since it is a prime and (12*29 - 1, 12*29 + 1) = (347, 349) and (18*29 - 1, 18*29 + 1) = (521, 523) are twin primes.
1051 is a term since it is a prime and (12*1051 - 1, 12*1051+ 1) = (12611, 12613) and (18*1051 - 1, 18*1051 + 1) = (18917, 18919) are twin primes.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A138242 and A138248.

Cf. A001097, A001359, A006512.

Programs

Magma

[p: p in PrimesUpTo(100000)| IsPrime(12*p-1) and IsPrime(12*p+1) and IsPrime(18*p-1) and IsPrime(18*p+1)]; // Vincenzo Librandi, Nov 24 2010

Mathematica

a=12;b=18;Select[Prime[Range[14^4]],PrimeQ[a*#-1]&&PrimeQ[a*#+1]&&PrimeQ[b*#-1]&&PrimeQ[b*#+1]&]
Select[Prime[Range[30000]],AllTrue[{12#-1,12#+1,18#-1,18#+1},PrimeQ]&] (* Harvey P. Dale, Dec 31 2024 *)

Extensions

More terms from Vincenzo Librandi, Apr 01 2010