A107022 Primes p such that 2p+1, 4p+3, 6p+5, 8p+7, 10p+9 are all primes.

2, 6449, 210209, 244589, 528509, 810539, 968729, 985109, 1316699, 1551899, 1743419, 2832629, 4094999, 4328459, 5608409, 6036869, 7077419, 7939829, 8176979, 8673569, 8789279, 9080189, 9797279, 10122419, 10309889, 10487969

Offset: 1

Author

Zak Seidov, May 09 2005

Keywords

• nonn

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A107024: p, 2p+1, 4p+3, 6p+5, 8p+7, 10p+9, 12p+11, 14p+13 all prime; A107023: p, 2p+1, 4p+3, 6p+5, 8p+7, 10p+9, 12p+11 all prime; A107021: p, 2p+1, 4p+3, 6p+5, 8p+7 all prime;A107020: p, 2p+1, 4p+3, 6p+5 all prime; A007700: p, 2p+1, 4p+3 all prime; A005384: p, 2p+1 prime (p = Sophie Germain primes).

Cf. A005384, A007700, A107020, A107021, A107023, A107024.

Programs

Magma

[p: p in PrimesUpTo(100000000)| IsPrime(2*p+1) and IsPrime(4*p+3) and IsPrime(6*p+5) and IsPrime(8*p+7)and IsPrime(10*p+9)]; // Vincenzo Librandi, Nov 13 2010

Mathematica

Select[Prime[Range[700000]],And@@PrimeQ[{2#+1,4#+3,6#+5,8#+7,10#+9}]&] (* Harvey P. Dale, Jun 19 2013 *)
Select[Prime[Range[700000]],AllTrue[Table[2n #+2n-1,{n,5}],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 22 2018 *)

Extensions

More terms from Vincenzo Librandi, Apr 01 2010