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%I #14 Jan 18 2024 18:43:42
%S 1564,4057,4654,5884,26599,30139,37204,66532,74227,80812,98137,113929,
%T 124249,138604,245524,249847,250879,299767,309469,315277,340504,
%U 346279,359467,362674,367069,401407,410332,435049,437377,438799,537844,550582,579814,587047
%N Integers n such that p = 4n + 1, q = 4p + 3, r = 4q + 5, s = 4r + 7 and t = 4s + 9 are all prime.
%C The first prime n is 4057.
%H Zak Seidov, <a href="/A243528/a243528_1.txt">Table of first 30 values of n, p, q, r, s, t.</a>
%e First 3 values of n, p, q, r, s and t:
%e {1564, 6257, 25031, 100129, 400523, 1602101},
%e {4057, 16229, 64919, 259681, 1038731, 4154933},
%e {4654, 18617, 74471, 297889, 1191563, 4766261}.
%t pqrstQ[n_]:=Module[{p=4n+1,q,r,s},q=4p+3;r=4q+5;s=4r+7;AllTrue[{p,q,r,s,4s+9},PrimeQ]]; Select[Range[590000],pqrstQ] (* _Harvey P. Dale_, Jan 18 2024 *)
%o (Magma) A141291:=func<h | (5*4^h-6*h-5) div 9>; [n: n in [1..10^6] | forall{i: i in [1..5] | IsPrime(4^i*n + A141291(i))}]; // _Bruno Berselli_, Jun 06 2014
%K nonn
%O 1,1
%A _Zak Seidov_, Jun 06 2014
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