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Primes that remain prime through 4 iterations of function f(x) = 6x + 5.
2

%I #22 Sep 08 2022 08:44:47

%S 11,13,83,151,317,373,1721,3529,4153,4243,4637,4783,5209,5849,5923,

%T 6661,8431,10903,11329,14519,16183,16979,20149,26669,27509,27827,

%U 29873,29947,32987,33637,33937,34919,35099,35543,36277,36691,38069,38461,41651,47407

%N Primes that remain prime through 4 iterations of function f(x) = 6x + 5.

%C Primes p such that 6*p+5, 36*p+35, 216*p+215 and 1296*p+1295 are also primes. - _Vincenzo Librandi_, Aug 04 2010

%H John Cerkan, <a href="/A023317/b023317.txt">Table of n, a(n) for n = 1..10000</a>

%t if4Q[n_]:=AllTrue[Rest[NestList[6#+5&,n,4]],PrimeQ]; Select[Prime[ Range[ 5000]],if4Q] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, May 10 2018 *)

%o (Magma) [n: n in [1..1000000] | IsPrime(n) and IsPrime(6*n+5) and IsPrime(36*n+35) and IsPrime(216*n+215) and IsPrime(1296*n+1295)] // _Vincenzo Librandi_, Aug 04 2010

%Y Subsequence of A023221, A023257, A023288, and A059325.

%K nonn

%O 1,1

%A _David W. Wilson_