login
Primes p such that 2p+1, 4p+3, 6p+5 are all primes.
5

%I #23 Feb 10 2024 03:01:28

%S 2,11,41,1901,2459,5081,5849,6131,6449,8969,9221,10691,12119,13229,

%T 14009,14321,14669,15161,18461,19709,20411,21179,22271,23099,24551,

%U 25601,30389,37991,39419,41381,43691,44699,52289,55631,56081,58979

%N Primes p such that 2p+1, 4p+3, 6p+5 are all primes.

%H Donovan Johnson, <a href="/A107020/b107020.txt">Table of n, a(n) for n = 1..1000</a>

%t Select[Range[60000],AllTrue[{#,2#+1,4#+3,6#+5},PrimeQ]&] (* _James C. McMahon_, Feb 09 2024 *)

%o (Magma) [p: p in PrimesUpTo(1000000)| IsPrime(2*p+1) and IsPrime(4*p+3) and IsPrime(6*p+5) ]; // _Vincenzo Librandi_, Nov 13 2010

%Y 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; A107022: p, 2p+1, 4p+3, 6p+5, 8p+7, 10p+9 all prime; A107020: p, 2p+1, 4p+3, 6p+5, 8p+7 all prime; A007700: p, 2p+1, 4p+3 all prime; A005384: p, 2p+1 prime (p = Sophie Germain primes).

%Y Cf. A005384, A007700, A107021, A107022, A107023, A107024.

%K nonn

%O 1,1

%A _Zak Seidov_, May 09 2005

%E More terms from _Vincenzo Librandi_, Apr 01 2010