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%I #4 Dec 31 2018 18:15:39
%S 47,1439,2879,858239,861599,982559,1014719,1067999,2029439,2034239,
%T 2297759,2683679,2978399,3301919,4068479,4288799,4737599,5454719,
%U 6484319,6753119,7145759,8624159,9511199,9717119,10533599,10739999
%N Quatro-safe primes.
%C (47-1)/2=23,(23-1)/2=11,(11-1)/2=5,(5-1)/2=2(prime),...
%t lst={};Do[p=Prime[n];If[PrimeQ[a=(p-1)/2]&&PrimeQ[b=(a-1)/2]&&PrimeQ[c=(b-1)/2]&&PrimeQ[(c-1)/2],AppendTo[lst,p]],{n,10!}];lst
%t Select[Prime[Range[711000]],AllTrue[Rest[NestList[(#-1)/2&,#,4]], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Dec 31 2018 *)
%Y Cf. A005385, A066179, A157357, A157358
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Feb 27 2009